Question

Assertion (A): $$(x - 1)$$ is a factor of $$x^3 + 2x^2 - x - 2$$.

Reason (R): If $$(x + \alpha)$$ is a factor of $$f(x)$$, then $$f(\alpha) = 0$$.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is true, but R is false.

Explanation:

$$f(1) = 1^3 + 2(1)^2 - 1 - 2 = 0$$, so $$x - 1$$ is a factor; A is true. However, factor theorem says $$(x + \alpha)$$ is a factor if $$f(-\alpha) = 0$$, not $$f(\alpha) = 0$$; hence R is false.