Question

Which of the following best describes the relationship between (x + 1) and the polynomial -3x3 - 2x2 + 1?

A.
(x + 1) is a factor.

B.
It is impossible to tell whether (x + 1) is a factor.

C.
(x + 1) is not a factor.

Answer 1

(C) (x+1) is not a factor

Explanation:

To show that x+1 is not a factor, in other words to show that the polynomial cannot be written as a product

`(x+1)\cdot(some\,\,quadratic)=-3x^3-2x^2+1`

it suffices to test that x=-1 is not a root of the original cubic:

`-3x^3-2x^2+1|_(x=-1)=-3(-1)^3-2(-1)^2+1=2\\eq 0`

which is hereby shown and the option (A) is out.

Option (B) is non-sense.

Option (C) is the correct answer.