Algebra II, Chapter 5
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
