What is the factored form of the binomial expansion x4 – 16x3 + 96x2 – 256x + 256?

Mathematics

1 answer:

navik [9.2K]3 years ago

7 0

Answer:

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

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