Answer:
<h2>
(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4</h2>
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−<em>8x^3</em>+<u>16x^2</u>−8x^3+<u>64x^2</u>−<em>128x</em>+<u>16x^2</u>−<em>128x</em>+<u><em>256</em></u>=
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