Question

Completely factor the polynomial

4x^3+16x^2+4x+16

Answer 1

can you see the GCF of the 4 terms?

Answer 2

4x?

Answer 3

no - because of the 16
GCF = 4

Answer 4

ok so that drops off the x because no x is in that term

Answer 5

so we get
4(x^3 + 4x^2 + x + 4)

Answer 6

now you need to factor the parentheses
as last term is 4 x+ 2 or x+ 4 are possible factors
if x+ 2 is a factor then f(-2) = 0

Answer 7

OK that part confuses me how does it change the last part of it

Answer 8

i'm applying the factor theorem
- if x-a is a factor of f(x) then f(a) = 0

Answer 9

if (x+a) is a factor then f(-a) = 0

Answer 10

i 'll try to see if (x+4) is a factor of the polynomial we have :

f(-4) = (-4)^3 + 4(-4)^2 - 4 + 4
= -64 + 64 - 4 + 4 = 0

Answer 11

that means (x + 4) is one of the factors

Answer 12

to find the other factors we need to divide the polynomial by x+4