Question

Factor completely x^8-16

A.) (x^4 - 4) ( x^4 + 4)

B.) ( x^2 - 2) ( x^2 + 2) (x^4+4)

C.) (x^2 - 2) (x^2 + 2) (x^4-4)

D.) (x^2-2) (x^2-2) (x^4-4)

Answer 1

B.) ( x^2 - 2) ( x^2 + 2) (x^4+4)

Explanation:

x⁸ - 16

(x⁴)² - 4²

(x⁴ - 4)(x⁴ + 4)

[(x²)² - 2²](x⁴ + 4)

(x² - 2)(x² + 2)(x⁴ + 4)

Answer 2

(x^2 -2) (x^2+2) (x^4 +4)

Explanation:

x^8-16

We know this is the difference of squares a^2 -b^2 = (a-b)(a+b)

x^4 ^2 - 4^2 =(x^4 -4) (x^4 +4)

We also recognize the x^4 -4 is the difference of squares

(x^2^2 -2^2) (x^4 +4)

(x^2 -2) (x^2+2) (x^4 +4)