Using synthetic division, determine whether the numbers are zeros of the polynomial function.-1, 2; h(x)=x+3x³ + 2x² - 6x-6Is -1 a zero of h(x)=x+3x3 + 2x² - 6x-6?O NoYesIs 2 a zero of h(x) = x² + 3x³ + 2x² - 6x-6?NoYes00

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Answered: Using synthetic division, determine…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section: Chapter Questions

Problem 8T: Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result...

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Similar questions

(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.
Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result to factor the polynomial function completely and list all the zeros of the function.
Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.
Write a third-degree polynomial function with real coefficients and the given zeros. 4,i
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
True or False? If c is a real zero of the polynomial P, then all the other zeros of P are zeros of P(x)/(xc).
Use the Remainder Theorem to find the remainder when f(x)=x37x+12 is divided by x+3 .
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.
If we divide the polynomial P by the factor xc and we obtain the equation P(x)=(xc)Q(x)+R(x), then we say that xc is the divisor, Q(x) is the _________, and R(x) is the ________.
Height of Projectile The height (in feet) of an object projected upward is given by the polynomial 16t2+60t+90 where t represents time in seconds. Find the height after t=2.5 seconds.
The polynomial 6x2+15xy gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x=5 feet and y=8 feet.

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Using synthetic division, determine whether the numbers are zeros of the polynomial function. -1, 2; h(x)=x+3x³ + 2x² - 6x-6 Is -1 a zero of h(x) = x + 3x³ + 2x² - 6x-6? O No Yes Is 2 a zero of h(x) = x+3x³ + 2x² - 6x-6? O No Yes