29.8k views
4 votes
What is the factored form of the binomial expansion x4 – 16x3 + 96x2 – 256x + 256?

User Ver
by
5.3k points

1 Answer

2 votes

Answer:

(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4

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^48x^3+16x^28x^3+64x^2128x+16x^2128x+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

User Skillz
by
4.9k points