Factor x^3 - 8.

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Multiple Choice

Factor x^3 - 8.

Explanation:
When you see x^3 minus 8, recognize it as a difference of cubes. The cube of x is x^3 and the cube of 2 is 8, so use a^3 − b^3 = (a − b)(a^2 + ab + b^2). With a = x and b = 2, you get (x − 2)(x^2 + 2x + 4). Expanding confirms it: x(x^2 + 2x + 4) − 2(x^2 + 2x + 4) = x^3 − 8. The other options don’t match this pattern or fail the expansion, so this is the correct factorization.

When you see x^3 minus 8, recognize it as a difference of cubes. The cube of x is x^3 and the cube of 2 is 8, so use a^3 − b^3 = (a − b)(a^2 + ab + b^2). With a = x and b = 2, you get (x − 2)(x^2 + 2x + 4). Expanding confirms it: x(x^2 + 2x + 4) − 2(x^2 + 2x + 4) = x^3 − 8. The other options don’t match this pattern or fail the expansion, so this is the correct factorization.

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