Question

Which expression is equivalent to this polynomial? x² + 8

A. (x + 2√2)(x - 2√2)
B. (x + 4i)(x - 4i)
C. (x + 2√2)²
D. (x + 2√2i)(x - 2√2i)

Answer 1

The equivalent expression is (x + 2√2)(x - 2√2) because it uses the difference of squares formula and simplifies back to the original polynomial x² + 8.

Step-by-step explanation:

The expression x² + 8 can be factored into a product of two binomials using the difference of squares approach, since 8 is a perfect square (2√2²). The correct factorization is (x + 2√2)(x - 2√2). This is because when you multiply these two binomials, the inner and outer terms cancel out, leaving x² - (2√2)², which simplifies back to x² + 8. Therefore, the equivalent expression to the polynomial x² + 8 is Option A: (x + 2√2)(x - 2√2).