Find polynomial with given zeros and degree calculator. Learn how to write a polynomial both in factored form an...

By the Rational Zeroes Theorem, any rational solution must be a

Step 1: Use rational root test to find out that the x = 1 is a root of polynomial x3 +9x2 + 6x −16. The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction qp , where p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is 16, with a single factor ...To express this polynomial as a product of linear factors you have to find the zeros of the polynomial by the method of your choosing and then combine the linear expressions that yield those zeros. , but then you are left to sort through the thrid degree polynomial. We can quickly synthetically divide the polynomial . So that's.Precalculus questions and answers. Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and zeros 2+i and 2−i. P (x)= [−/2.94 Points ] SPRECALC7 3.5.039.MI. Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 2, 5i, and −5i.Expert Answer. Transcribed image text: 4.3.19 Question Help 0 Find a polynomial function P (x) having leading coefficient 1, least possible degree, real coefficients, and the given zeros. - 11 and 8 P (x)= (Simplify your answer.)Question: Find a polynomial function P(x) of degree 3 with real coefficients that satisfies the given conditions. Do not use a calculator. Zeros of −7,1, and 0;P(−2)=−15 P(x)= (Simplify your answer. Use integers or fractions for any numbers in the expression.)Find a polynomial function P(x) having leading coefficient 1 , least possible degree, real coefficients, andFind the nth-degree polynomial function with real coefficients satisfying the given conditions. n=3. 4 and 5i are zeros. f(2)=116. Answer provided by our tutors since complex roots only occur in complex conjugate pairs if 5i is root that - 5i is root as well.Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Zeros of a Polynomial | Desmosexample 1: Find a polynomial that has zeros . example 2: Find the polynomial with integer coefficients having zeroes and . example 3: Which polynomial has a double zero of and has as a simple zero? example 4: Find a polynomial that has zeros and . Search our database of more than 200 calculators Was this calculator helpful? Yes No This calculator finds out where the roots, maxima, minima and inflections of your function are.Step-by-Step Examples. Algebra. Simplifying Polynomials. Use the Rational Roots Test to Find All Possible Roots. x3 − 1 x 3 - 1. If a polynomial function has integer coefficients, then every rational zero will have the form p q p q where p p is a factor of the constant and q q is a factor of the leading coefficient. p = ±1 p = ± 1. q = ±1 ...The multiplicity of a zero is important because it tells us how the graph of the polynomial will behave around the zero. For example, notice that the graph of f (x)= (x-1) (x-4)^2 f (x) = (x −1)(x −4)2 behaves differently around the zero 1 1 than around the zero 4 4, which is a double zero.Mar 28, 2021 ... Finding a Polynomial: Without Non-zero Points Example. Find a polynomial of degree 4 with zeroes of -3 and 6 (multiplicity 3). Step 1: Set up ...👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . ...A "root" is when y is zero: 2x+1 = 0. Subtract 1 from both sides: 2x = −1. Divide both sides by 2: x = −1/2. And that is the solution: x = −1/2. (You can also see this on the graph) We can also solve Quadratic Polynomials using basic algebra (read that page for an explanation). 2. By experience, or simply guesswork.A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general defintion of a polynomial, and define its degree. 2. What is a polynomial? A polynomial of degree n is a function of the form f(x) = a nxn +a n−1xn−1 +...+a2x2 +a1x+a0Sayed S. asked • 04/15/20 Find the polynomial function of degree 3 with real coefficients that satisfies given conditions; zero of −4 and zero of 0 having multiplicity 2 where 𝑓(−1) = 6O POLYNOMIAL AND RATIONAL FUNCTIONS Finding a polynomial of a given degree with given zeros: Real... Find a polynomial f(x) of degree 5 that has the following zeros. 7 - 2, 8, 1, - 4 Leave your answer in factored form. x 5 ?This video explains how to determine the equation of a polynomial function in factored form and expanded form from the zeros.http://mathispower4u.comForm a polynomial whose zeros and degree are given. Zeros: −7 , multiplicity 1; −4 , multiplicity 2; degree 3. Question content area bottom Part 1. Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below. f(x)=enter your response here (Simplify your answer.)Multiply a chain of factors of the form (x - r 1)(x - r 2)... where the r's are the zeros.For (1 + i), its complex conjugate must also be a zero. You will have 4 different zeros, and hence a polynomial of minimum degree 4.The polynomial can be written as. ( x + 3) ( 3 x 2 + 1) We can then set the quadratic equal to 0 and solve to find the other zeros of the function. 3 x 2 + 1 = 0 x 2 = − 1 3 x = ± − 1 3 = ± i 3 3. The zeros of f ( x) are - 3 and ± i 3 3. Analysis. Look at the graph of the function f in Figure 5.6. 2.May 22, 2023 · Welcome to Omni's polynomial graphing calculator, where we'll study how to graph polynomial functions. Obviously, the task gets more and more difficult when we raise the degree, and it becomes really complicated from five upwards. That's why we'll focus on polynomial function equations of degree at most four, where we're able to find the zeros ... Instructions: Use calculator to find the polynomial zeros, showing all the steps of the process, of any polynomial you provide in the form box below. Enter the polynomial you want to find roots for: (Ex: p(x) = x^4 + x^3 - 3x^2 + 2x - 1, etc.)Sayed S. asked • 04/15/20 Find the polynomial function of degree 3 with real coefficients that satisfies given conditions; zero of −4 and zero of 0 having multiplicity 2 where 𝑓(−1) = 6Expert Answer. 1. According to the Factor Theorem, the Expression (x-c) is a Factor of a Polynomial if and only if P (c)=0 Lets Consider a Polynomial Function P (x): If c=-2 is a ze …. Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros-2, 0, 2, 4 P (x) = Need Help?Algebra questions and answers. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answ 5,5,1 + 1 f (x) = x Need Help? Read It Submit Answer 12. [-76.25 Points) DETAILS LARPCALC10 2.5.047. Find the polynomial function with real coefficients that has the given degree, zeros, and solution point.Since we know the roots of the polynomial. we can begin to build the smallest polynomial using the Fundamental Theorem of Algebra (FTA)... Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root.. This leads to a polynomial of ... p(x) = (x - 5)(x - (4+i))(x - (4-i))Answer to Solved Find a polynomial of least degree with only real. Skip to main content ... Find a polynomial of least degree with only real coefficients and having the given zeros. OA. f(x) -x3-2x -19x-30 OB. f(x)=x3-2x2-19x + 24 c. f(x)=x3 + 2x2-19x +30 D. f(x)=x3 + 4x2-20x +30 Click to select your answer. ... Previous question Next question ...are multiple polynomials that will work. In order to determine an exact polynomial, the “zeros” and a point on the polynomial must be provided. Examples: Practice finding polynomial equations in general form with the given zeros. Find an* equation of a polynomial with the following two zeros: = −2, =4 Precalculus. Precalculus questions and answers. Find a polynomial f (x) that has the given degree and given zeros and that satisfies the given condition. Leave fin factored form. degree 3; zeros -8, 4, 22; f (2) = 1600 Find a polynomial f (x) with leading coefficient 1 and having the given degree and zeros. degree 3; zeros -1, 0,5.Jul 5, 2022 · For example, the polynomial P(x) = 2x² - 2x - 12 has a zero in x = 3 since: P(1) = 2*3² - 2*3 - 12 = 18 - 6 - 12 = 0. Finding the root is simple for linear equations (first-degree polynomials) and quadratic equations (second-degree polynomials), but for third and fourth-degree polynomials, it can be more complicated. There are formulas for ... Zeros of a polynomial calculator - Polynomial = 3x^2+6x-1 find Zeros of a polynomial, step-by-step online We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies.👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . ...This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 5, 3i, and −3i. Q (x)=.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Question. Construct the lowest-degree polynomial given the zeros below. Question. Construct the lowest-degree polynomial given the zeros below. f (a)- Question.So with the root of -2i given, we want its conjugate root of 2i. So the roots are. x = 1. → x - 1 = 0, x = - 2i. → x + 2i = 0, and. x = 2i. → x - 2i = 0. → f(x) = (x - 1)(x + 2i)(x - 2i), which I will expand. Multiply the quantities with the complex roots together first, as terms will cancel, and make the final multiplication easier,Title: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. Full text: n=3-3 and 2+2i are zeros. f(1)=20. Use the Linear Factorization Theorem to Find Polynomials With Given Zeros. Anybody know any calculator apps that'll help?*You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point.Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point. Degree Zeros 4 (x)=−1,2,2i.Expert Answer. Transcribed image text: Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point. Degree 3 Zeros -2,1-√21 Solution Point f (-1) = -54 f (x) = Need Help?Since we know the roots of the polynomial. we can begin to build the smallest polynomial using the Fundamental Theorem of Algebra (FTA)... Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root.. This leads to a polynomial of ... p(x) = (x - 5)(x - (4+i))(x - (4-i))Learn how to write a polynomial both in factored form and standard form when given the zeros of the function, and the multiplicity of each zero. Remember mu...Jul 27, 2020 · $\begingroup$ @N.F.Taussig I understand that they are the points where a smooth continuis polynomial function cross the x axis, each time corresponding to one of the factors with the local behavior of that factor e.g. straight intercept (degree 1), bounce (even degree) or a squiggle (odd degree) $\endgroup$ – How do you solve polynomials equations? To solve a polynomial equation write it in standard form (variables and canstants on one side and zero on the other side of the equation). Factor it and set each factor to zero. Solve each factor. The solutions are the solutions of the polynomial equation. How do you solve polynomials equations? To solve a polynomial equation write it in standard form (variables and canstants on one side and zero on the other side of the equation). Factor it and set each factor to zero. Solve each factor. The solutions are the solutions of the polynomial equation.Polynomials can have zeros with multiplicities greater than 1.This is easier to see if the Polynomial is written in factored form. 𝑃( )=𝑎( − 1) ( − 2) …( − 𝑖)𝑝 Multiplicity - The number of times a "zero" is repeated in a polynomial. The multiplicity of each zero is inserted as an exponent of the factor associated with the zero.Precalculus questions and answers. Find a polynomial function P (x) of degree 3 with real coefficients that satisfies the given conditions. Do not use a calculator. Zeros of -5.1, and 0; P (-2) - - 9 P (x)=0 (Simplify your answer. Use integers or fractions for any numbers in the expression.)Determining the positive and negative intervals of polynomials. Let's find the intervals for which the polynomial f ( x) = ( x + 3) ( x − 1) 2 is positive and the intervals for which it is negative. The zeros of f are − 3 and 1 . This creates three intervals over which the sign of f is constant:Form a polynomial whose real zeros and degree are given. Zeros: -1 , 0, 9 ; degree: 3 Type a polynomial with integer coefficients and a leading coefficient of 1.You can put this solution on YOUR website! find a polynomial of the specified degree: degree 4, zeros:-5,0,5,7. P (x)=. ---------------- 1. Put x= before each zero: x=-5; x=0, x=5, x=7 2. Get 0 on the right of each of the 4 equations: x+5=0; x=0; x-5=0; x-7=0 3. Indicate that the multiplication (product) of all the left sides equals the ...Form a polynomial with given zeros and degree multiplicity calculator. ... Polynomial ">How to Find Zeros & Their Multiplicities Given a Polynomial. ) f(x) = x4 ...Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . .... 👉 Learn how to write the equation of a polynomial when given irrational zeros.Solution: By the Fundamental Theorem of Algebra, since the degree of the polynomial is 4 the polynomial has 4 zeros if you count multiplicity. There are three given zeros of -2-3i, 5, 5. The remaining zero can be found using the Conjugate Pairs Theorem. f (x) is a polynomial with real coefficients. Since -2-3i is a complex zero of f (x) the ...Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero (0) is called zero polynomial. The degree of a polynomial is the highest power of the variable x. A polynomial of degree 1 is known as a linear polynomial. The standard form is ax + b, where a and b are real numbers ...A polynomial is an expression of two or more algebraic terms, often having different exponents. Adding polynomials... Read More. Save to Notebook! Sign in. Free Polynomial Leading Coefficient Calculator - Find the leading coefficient of a polynomial function step-by-step. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1 , and zeros of 4 and 3+i. The polynomial function is f (x)= (Simplify your answer.)k = – n / m It can be written as, Zero polynomial K = – (constant / coefficient (x)) How to Find the Zeros of a Function? Find all real zeros of the function is as simple as isolating …Find a polynomial function of lowest degree with real coefficients that are stated. Write the function in standard form. Zeros: 3, -2, and 1 ... Easy: just write the polynomial in factored form: P(x) = (x-1)(x+2)(x-3). It can be seen that the stated zeros are 1, -2 and 3 because each of them will make one of the factors zero.Find a polynomial function of lowest degree with real coefficients and the numbers 6, \ 3i as some of its zeros. Find a polynomial of degree 3 that has zeros: -2,1+2i,1-2i. Find a polynomial of degree 3 given zeros = -2, 1, 0 and P(2) = 32. Find a polynomial of degree n that has the given zero(s). x=0,\sqrt{3},-\sqrt{3} n=3How to Use Polynomial Degree Calculator? Please follow the below steps to find the degree of a polynomial: Step 1: Enter the polynomial in the given input box. Step 2: Click on the "Find" button to find the degree of a polynomial. Step 3: Click on the "Reset" button to clear the fields and find the degree for different polynomials. When any complex number with an imaginary component is given as a zero of a polynomial with real coefficients, the conjugate must also be a zero of the polynomial. \(\PageIndex{11}\) Find a third degree polynomial with real coefficients that has zeros of \(5\) and \(−2i\) such that \(f (1)=10\).Find step-by-step Precalculus solutions and your answer to the following textbook question: Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros -2, 0, 2, 4.Step 1: Use rational root test to find out that the x = 1 is a root of polynomial x3 +9x2 + 6x −16. The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction qp , where p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is 16, with a single factor ...Solution for 3. Find a least degree polynomial function with real coefficients that has the given zeros. (The leading coefficient should be 1) 1,1 - 2i,1 - V5.Cubic Equation Calculator. An online cube equation calculation. Solve cubic equation , ax 3 + bx 2 + cx + d = 0 (For example, Enter a=1, b=4, c=-8 and d=7) In math algebra, a cubic function is a function of the form. f ( x) = ax + bx + cx + d where "a" is nonzero. Setting f x) = 0 produces a cubic equation of the form: ax.Find two additional roots. 1-\sqrt {10} \text { and } 2+\sqrt {2} 1− 10 and 2+ 2. Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n = 4; 2 (with multiplicity 2) and 3i are zeros; f (0) = 36. Assume that z z is a complex number and f (x) f (x) is a polynomial with real coefficients.Mar 31, 2019 · About this tutor ›. It must be a degree 3 polynomial with integer coefficients with zeros -8i and 7/5. if -8i is a zero, then +8i (it's conjugate) must also be a solution. So, tnis gives you. (x-8i) (x+8i) (x -7/5) multiply the first 2 factors. (x2-64i2) (x-7/5) = (x2 + 64) (x - 7/5), but you need integer coefficients, so, change x - 7/5 to ... Polynomial Factorization Calculator - Factor polynomials step-by-step We have updated our ... Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight ... Equation Given Roots; Inequalities. Linear; Quadratic ...You can find zeros of the polynomial by substituting them equal to 0 and solving for the values of the variable involved that are the zeros of the polynomial. Finding a polynomial’s zeros can be done in a variety of ways. The degree of the polynomial equation determines how many zeros the polynomial has. To determine the zeros of the ...This video covers 1 example on how to create a polynomial with real coefficients that have the given degree and using the designated zeros. Like, Subscribe &...Free Polynomial Degree Calculator - Find the degree of a polynomial function step-by-stepa. A polynomial object for which the zeros are required. b. a numeric value specifying an additional intercept. If given, the zeros of a - b are found. …. Not used by this method.Polynomial Roots. Find the roots (solutions) of quadratic, cubic, and higher-degree polynomial equations. Roots of a Complex Number, Unity. Calculate the nth roots of a complex number, which are used in complex analysis and trigonometry. Rotate Point. Rotate points in a coordinate plane by a specified angle, a fundamental operation in geometry.Question: Find a polynomial function of degree 3 with the given numbers as zeros. Assume that the leading coefficient is 1. -5,6i. -61 The polynomial function is f(x)= (Simplify your answer. Use integers or fractions for any numbers in the expression.) Find a polynomial function of degree 3 with the given numbers as zeros.write a polynomial function of least degree with given zeros calculator. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.How To: Given a graph of a polynomial function, write a formula for the function. Identify the x-intercepts of the graph to find the factors of the polynomial.; Examine the behavior of the graph at the x-intercepts to determine the multiplicity of each factor.; Find the polynomial of least degree containing all of the factors found in the previous step.We have to find the polynomial whose zeros and degree are as follows - Zeros = -2, 2, 8 Degree = 3 And leading coefficient is 1. The general form of a polynomial function is as follows- f (x) = a (x − c 1) (x − c 2) (x − c 3) … (x − c n) Step 2 Given that the zeros are -2, 2, 8 therefore the factors of the required polynomial are ...Solution: Since -2 + 3i is an imaginary number then -2 - 3i must also be one of the zeros. After expansion, the leading coefficient is A, which is 1. Therefore, the 3rd degree polynomial is x³ + 2x² + 5x - 26. Find an nth degree polynomial function with real coefficients satisfying the given conditions. n = 3; 2 and -2 + 3i are zeros; leading ...You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 2 − 3i and 1, with 1 a zero of multiplicity 2. R (x) =. Find a polynomial with integer coefficients that satisfies the given conditions.You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Find a polynomial function with the given real zeros whose graph contains the given point. Zeros: −5,0,1,2 Degree: 4 Point: (−21,−270) f (x)= (Type your answer in factored form. Use integers or fractions for any numbers in the ...Form a polynomial with given zeros and degree multiplicity calculator. For a polynomial, if #x=a# is a zero of the function, then # (x-a)# is a factor of the function. We have two unique zeros: #-2# and #4#. However, #-2# has a multiplicity of #2#, which means that the factor that correlates to a zero of #-2# is represented in the polynomial twice. The Fundamental Theorem Of Algebra. If f(x) is a polynomial of degree n > 0, then f(x) has at least one complex zero. Example 4.5.6. Find the zeros of f(x) = 3x3 + 9x2 + x + 3. Solution. The Rational Zero Theorem tells us that if p q is a zero of f(x), then p is a factor of 3 and q is a factor of 3.© 2023 Chillicothe News Constitution-Tribune, a CherryRoad Media Newspaper. All rights reserved.y = polyval (p,x) evaluates the polynomial p at each point in x . The argument p is a vector of length n+1 whose elements are the coefficients (in descending powers) of an n th-degree polynomial: p ( x) = p 1 x n + p 2 x n − 1 + ... + p n x + p n + 1. The polynomial coefficients in p can be calculated for different purposes by functions like ...This video covers 1 example on how to create a polynomial with real coefficients that have the given degree and using the designated zeros. Like, Subscribe &...Find a polynomial with integer coefficients that satisfies the given conditions.Q has degree 3 and zeros 5, 5i, and −5i. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.This calculator solves equations that are reducible to polynomial form. Some examples of such equations are 2(x + 1) + 3(x −1) = 5 , (2x + 1)2 − (x − 1)2 = x and 22x+1 + 33−4x = 1 . The calculator will show each step and provide a thorough explanation of how to simplify and solve the equation.Q: Given the graph of the following degree 5 polynomial function, find all of the zeros and their… A: From the graph we can say ,the polynomial has factors ,x+33 and x-12 . Q: Give 3 different reasons why the following graph cannot be the the graph of the polynomial with…Sal finds all the zeros (which is the same as the roots) of p (x)=x⁵+9x³-2x³-18x=0.. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Jamie Tran 8 years …When any complex number with an imaginary component is given as a zero of a polynomial with real coefficients, the conjugate must also be a zero of the polynomial. \(\PageIndex{11}\) Find a third degree polynomial with real coefficients that has zeros of \(5\) and \(−2i\) such that \(f (1)=10\).Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) -1, 8, 3 - 2i *(x) = y=x5 - 10x+ + 1773 - 16x2 + 52x + 96 This problem has been solved!Example \(\PageIndex{7}\): Using the Linear Factorization Theorem to Find a Polynomial with Given Zeros. Find a fourth degree polynomial with real coefficients that has zeros of \(–3\), \(2\), \(i\), such that \(f(−2)=100\). Solution. Because \(x =i\) is a zero, by the Complex Conjugate Theorem \(x =–i\) is also a zero. The polynomial must have …Dec 14, 2018 ... A 3rd degree polynomial has roots at x=-2i and x=5. The y-intercept is ... Given roots (real and complex), find the polynomial · 0 · Polynomial ...Can you help her in finding the degree and zeros of the following polynomial, \( x^2 - x - 6\) Solution. For the given polynomial, \( P(x) = x^2 - x - 6\) We know, Highest power of the variable \(x\) = 2. Thus, the degree of the polynomial = 2. To find the zeros of the polynomial, we will make it a polynomial equation and them use factorization: . Cubic Equation Calculator. An online cube equ👉 Learn how to write the equation of a p The Fundamental Theorem Of Algebra. If f(x) is a polynomial of degree n > 0, then f(x) has at least one complex zero. Example 3.5.6. Find the zeros of f(x) = 3x3 + 9x2 + x + 3. Solution. The Rational Zero Theorem tells us that if p q is a zero of f(x), then p is a factor of 3 and q is a factor of 3. First, we need to notice that the polynomial can be wr 👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . ...Solution. Step 1: Express the equation in standard form, equal to zero. In this example, subtract 5x from and add 7 to both sides. 15x2 + 3x − 8 = 5x − 7 15x2 − 2x − 1 = 0. Step 2: Factor the expression. (3x − 1)(5x + 1) = 0. Step 3: Apply the zero-product property and set each variable factor equal to zero. A polynomial is an expression of two or more algebraic terms,...

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