Answer:
(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4
Step-by-step explanation:
x^4 – 16x^3 + 96x^2 – 256x + 256
terms with odd exponents are negative
x^4 has a coefficient of one, so the expression's GCF is 1
Thus, we need to factor out the expression as it is:
(x-4)*(x-4)*(x-4)*(x-4)
Lets multiply it out to check:
(x-4)*(x-4)*(x-4)*(x-4)=
(x^2-8x+16)*(x^2-8x+16)=
x^4−8x^3+16x^2−8x^3+64x^2−128x+16x^2−128x+256=
x^4 – 16x^3 + 96x^2 – 256x + 256
thus, the factored form is:
(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4
