Question

$4x^3+4x^2-x-1$ is a multiple of

• A. 2x-1
• B. 2x+1
• C. x-1
• D. x-4

Answer 1

The correct option is B

2x+1

Let P(x) = $4x^3+4x^2-x-1$
Substitute from the options

$(x-a)$ is a factor of $P\left(x\right)$ if $P\left(a\right)$ = 0

Taking a as $-\frac{1}{2}$, we get:

P(a) = $-\frac{1}{2}+1+\frac{1}{2}-1$ = 0

Thus, 2x + 1 is a factor of $4x^3+4x^2-x-1$.

Hence, $4x^3+4x^2-x-1$ is a multiple of $2x+1$.