Question

Factor the polynomial completely.
x^4 – 256

Answer 1

(x²+16)(X+4)(x-4)

Explanation:

x⁴ can be written as (x²)²

256 can be written as (16)²

by identity. a²-b²= (a+b)(a-b) :

(x²+16)(x²-16)

x²-16 can be written as (x)²- 4²

by identity. a²-b²= (a+b)(a-b) :

(X+4)(x-4)

Therefore, the factors altogether would be

(x²+16)(x+4)(x-4)