2. Please solve with the full step and explanation thank u 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1,then the remainder of dividing f(x) by (x² + x – 12) is...A.f(-4)(x – 3) –(x + 4)+ 4)B.f(-4)(x – 3) +(x + 4)1ca + 4) -(-4)(x – 3)D.-(x + 4) +f(-4)x – 3)E. . -* + 4) -f(-4)(x – 3)

Answered: 2. If the polynomial f (x) divided by…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 38E

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Similar questions

A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.
Which of the following statements couldn't possibly be true about the polynomial function P? (a) P has degree 3, two local maxima, and two local minima. (b) P has degree 3 and no local maxima or minima. (c) P has degree 4, one local maximum, and no local minima.
If c is a zero of polynomial P. then (a) P(c) = __________. (b) xc is a__________of P(x). (c) c is a(n) _____-intercept of the graph of P.
The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
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?
a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant polynomial in Z3[ x ], if one exists, that is a unit. c. Prove or disprove that there exist nonconstant polynomials in Zp[ x ] that are units if p is prime.

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2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of dividing f(x) by (x² + x – 12) is... A.f(-4)(x – 3) –(x + 4) + 4) B.f(-4)(x – 3) +(x + 4) 1 ca + 4) -(-4)(x – 3) D.-(x + 4) +f(-4)x – 3) E. . -* + 4) -f(-4)(x – 3)