Question

select the correct answer.
what are the factors of polynomial function g?
g(x) = x³ + 2x² − x − 2
a. (x − 2)(x − 1)(x + 2)
b. (x − 2)(x − 1)(x + 1)
c. (x − 1)(x + 1)
d. (x − 1)(x + 1)(x + 2)

Explanation:

Step1: Factor by grouping

Group the terms: \( (x^3 + 2x^2) + (-x - 2) \)
Factor out common terms: \( x^2(x + 2) - 1(x + 2) \)

Step2: Factor out \( (x + 2) \)

We get: \( (x + 2)(x^2 - 1) \)

Step3: Factor \( x^2 - 1 \)

Using difference of squares (\( a^2 - b^2=(a - b)(a + b) \)): \( x^2 - 1=(x - 1)(x + 1) \)

Step4: Combine factors

So \( g(x)=(x - 1)(x + 1)(x + 2) \)

Answer:

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