Dividing Polynomials
(4x3-16x2+20x-16)/(x-3)
4x2-4x+8+(8/(x-3))
Use the Remainder Theorem to evaluate f(x) at c.
f(x)=-2x5+7x4+2x3-x+8; c=4
f(4)=-124
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+
(x3-49x+120)/(x+8)
x2-8x+15
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
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
(6x3-13x2+12x+6)/(3x-2)
2x2-3x+2+(10/(3x-2))
Find all zeros of the polynomial function.
f(x)=x4-4x2-12
x = i root 2, -i root 2, root 6, - root 6
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
(x4+3x3+4x2+24x-32)/(x2+8)
x2+3x-4
List all possible rational zeros. Then find all the zeros.
f(x)=x4-x3-12x2+28x-16
x = -4, 1, 2
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