Question

select the correct answer.

what are the factors of polynomial function \\(g\\)?

\\g(x) = x^3 + 2x^2 - x - 2\\

\\((x - 2)(x - 1)(x + 1)\\)

\\((x - 1)(x + 1)(x + 2)\\)

\\((x - 1)(x + 1)\\)

\\((x - 2)(x - 1)(x + 2)\\)

Explanation:

Group terms to factor by grouping

$$ g(x) = (x^3 + 2x^2) - (x + 2) $$

Factor out common terms from each group

$$ g(x) = x^2(x + 2) - 1(x + 2) $$

Factor out the common binomial and apply difference of squares

$$
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$$

Answer:

• (A) \((x - 2)(x - 1)(x + 1)\)
• (B) \((x - 1)(x + 1)(x + 2)\) (Correct answer)
• (C) \((x - 1)(x + 1)\)
• (D) \((x - 2)(x - 1)(x + 2)\)