Question

Find the zeros of the polynomial function.
f(x) = x^3 + 5x^2 - 4x - 20

Answer 1

Do you know how to factor by grouping?

Answer 2

I do but when three is x^3 it confuses me

Answer 3

I'll do the factor by grouping part for you.
\[x^3+5x^2-4x-20=x^2(x+5)-4(x+5)=(x^2-4)(x+5)\]Can you factor \(x^2-4\)?

Answer 4

(x - 2)(x +2)

Answer 5

Perfect. That means your polynomial factors like \[(x-2)(x+2)(x+5)\]What does this tell you about the zeros?

Answer 6

so they would be -2,2,5

Answer 7

Almost. Your zeros would be -2,2,-5

Answer 8

so I have to do this first
x+5=0
x=-5

Answer 9

Right.

Answer 10

then I get my zeros

Answer 11

thank you I just have a hard time factoring when the equation is like that

Answer 12

You're welcome.