Question

Factor completely 2x^4 − 32.

A) 2(x^2 − 4)(x^2 + 4)
B) 2(x − 2)(x + 2)(x^2 + 4)
C) 2(x − 2)(x + 2)(x + 2)(x + 2)
D) 2(x − 2)(x + 2)(x^2 − 4)

Answer 1

The expression 2x^4 - 32 can be factored completely as 2(x^2 - 4)(x^2 + 4).

Step-by-step explanation:

The given expression is 2x^4 - 32. To factor completely, we look for common factors. In this case, 2 is a common factor:

2(x^4 - 16)

We can then recognize that the expression inside the parentheses is a difference of squares, which can be factored as (a^2 - b^2) = (a + b)(a - b):

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

Therefore, the correct answer is option A) 2(x^2 - 4)(x^2 + 4).