Algebra II, Chapter 5

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Determine the end behavior of the graph of each polynomial function. 2x^2-3x^3+2x

up and down

Divide using long division. SHOW YOUR WORK!! (x^2-13x-48)/(x+3)

x-16

Write a polynomial function in standard form with the given zeros. x=-1,3,4

x^3-6x^2+5x+12

Write a polynomial function in standard form with the given zeros. x=-3,0,0,5

x^4-x^3-15x^2

Determine whether each binomial is a factor of... x^3+3x^2-10x-24 (x+4)

yes

Determine whether each binomial is a factor of... x^3+3x^2-10x-24 (x-3)

yes

Write each polynomial in factored form. x^3+7x^2+2x+14

(x^2+2)(x+7)

Use synthetic division and the remainder theorem to find P(a). P(x)=x^3+7x^2+12x-3;a=-5

P(-5)=-13

Write each polynomial in standard form. Then classify by degree and number of terms. x^2-2x^3+9-x

SF: -2x^3+x^2-x+9 D: cubic T: polynomial

Find the zeros of each function then sketch the graph to illustrate the zeros and end behavior. y=(x+3)(x-2)(x+4)

zeros: -3,2,-4 sketch: from left to right, down and up

Find the zeros of each function then sketch the graph to illustrate the zeros and end behavior. y=(x+4)(x-3)

zeros: -4,3 sketch: u-shape facing up

Find the zeros of each function. State the multiplicity of multiple zeros. y=x(x+3)^3(x-1)

zeros: 0,3,3,3,1 -3 multiplicity of 3

Find the zeros of each function then sketch the graph to illustrate the zeros and end behavior. y=(x-2)(x+1)

zeros: 2,-1 sketch: u-shape facing up

Find the zeros of each function then sketch the graph to illustrate the zeros and end behavior. y=(x-5)(x+3)(x-2)

zeros: 5,-3,2 sketch: from left to right, down and up

Find the zeros of each function. State the multiplicity of multiple zeros. y=(x-5)(x+2)^2

zeros: 5,2,2 -2 multiplicity of 2

Use synthetic division and the given factor to completely factor each polynomial function. y=x^3+3x^2-13x-15;(x+5)

(x+1)(x-3)(x+5)

Use synthetic division and the given factor to completely factor each polynomial function. x^3-3x^2-10x+24;(x-2)

(x+3)(x-4)(x-2)

Find the real or imaginary solutions of each equation by factoring. x^4-12x^2+11=0

+/-1 and +/-(11) ()=square root

Find the real or imaginary solutions of each equation by factoring. x^4-10x^2+9=0

+/-1 and +/-3

Divide using synthetic division. SHOW YOUR WORK!! (-2x^3+15x^2-22x-15)/(x-3)

-2x^2+9x+5

Write each polynomial in factored form. -3x^3+18^2-27x

-3x(x-3)(x-3)

Find the real or imaginary solutions of each equation by factoring. x^3+64=0

-4 and 2+/-2i(3) ()=square root

What does Descartes' Rule of Signs say about the number of positive and negative real roots for each polynomial function? P(x)=3x^3+x^2-8x-12

1 poss. pos. real roots; 2,0 poss. neg. real roots

What does Descartes' Rule of Signs say about the number of positive and negative real roots for each polynomial function? P(x)=2x^4-x^3-3x+7

2,0 poss. pos. real roots; 0 poss. neg. real roots

Write each polynomial in factored form. 2x^3+10x^2+12x

2x(x+2)(x+3)

Find the real or imaginary solutions of each equation by factoring. 8x^3-27=0

3/2 and 3+/-3i(3)/4 ()=square root

Divide using long division. SHOW YOUR WORK!! (3x^3-x^2-7x+6)/(x+2)

3x^2-7x+7-8/(x+2)

Write each polynomial in standard form. Then classify by degree and number of terms. 2x-4x+9-3x^2

SF: -3x^2-2x+9 D: quadratic T: trinomial

Write each polynomial in standard form. Then classify by degree and number of terms. x^2-5x+3x^5-2+4x^3

SF: 3x^5+4x^3+x^2-5x-2 D: quintic T: polynomial

Write each polynomial in standard form. Then classify by degree and number of terms. 9x^4

SF: 9x^4 D: quartic T: monomial

Use the rational root theorem to list all the possible rational roots for each equation. 36x^3+144x^2-x-4=0

p/q= +/-1,+/-4,+/-2,+/-1/36,+/-1/9,+/-1/18,+/-1/2,+/-2/9, +/-1/3,+/-4/3,+/-2/3,+/-1/12,+/-1/6,+/-1/4,+/-4/9, +/-2/9

Determine the end behavior of the graph of each polynomial function. -2x^6-3x^2+8

down and down

Determine the end behavior of the graph of each polynomial function. 5x+1

down and up

Use synthetic division and the remainder theorem to find P(a). P(x)=3x^3-4x^2-5x+1;a=2

p(2)=-1

Use the rational root theorem to list all the possible rational roots for each equation. x^3+5x^2-2x-15=0

p/q= +/-1,+/-15,+/-3,+/-5

Determine the end behavior of the graph of each polynomial function. x^4+5x-2

up and up

Write each polynomial in factored form. x^3-2x^2+x

x(x-1)(x-1)

Divide using synthetic division. SHOW YOUR WORK!! (x^3-8x^2+17x-10)/(x-5)

x^2-3x+2


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