Trig/College Alg Honors 5.4-5.6 Review

Dividing Polynomials

200

(4x³-16x²+20x-16)/(x-3)

4x²-4x+8+(8/(x-3))

400

(x³-49x+120)/(x+8)

x²-8x+15

800

(6x³-13x²+12x+6)/(3x-2)

2x²-3x+2+(10/(3x-2))

600

(x⁴+3x³+4x²+24x-32)/(x²+8)

x²+3x-4

Zeros of Polynomial Functions

200

Use the Remainder Theorem to evaluate f(x) at c.

f(x)=-2x⁵+7x⁴+2x³-x+8; c=4

f(4)=-124

400

Use the Factor Theorem and the given binomial to completely factor the polynomial function.

f(x)=9x⁴-18x³-73x²+2x+8; (x+2)

x = -2, 1/3, -1/3, 4

800

Find all zeros of the polynomial function.

f(x)=x⁴-4x²-12

x = i root 2, -i root 2, root 6, - root 6

600

List all possible rational zeros. Then find all the zeros.

f(x)=x⁴-x³-12x²+28x-16

x = -4, 1, 2

Rational Functions

200

Using the graph on Warm Up Slide #1, use limit notation to describe the end behavior and local behavior of the function.

lim f(x) = 1

x->-oo

lim f(x) = 1

x->oo

lim f(x) = -oo

x->-3^-

lim f(x) = oo

x->-3⁺

400

For the following function, determine any vertical asymptotes, horizontal asymptotes, or holes.

f(x)= (x²-2x-15)/(x+3)

VA: None

HA: None

Hole: x=-3

800

For the following function, determine any vertical asymptotes, horizontal asymptotes, or holes.

f(x)=(x-1)/(x³-x²)

VA: x=0

HA: y=0

Hole: x=1

600

For the following function, determine any vertical asymptotes, horizontal asymptotes, or holes.

f(x)=[(x+2)(x-3)²]/[(x+2)²(x+5)]

VA: x=-2, x=-5
HA: y=1
Hole: None