Question

Select the option that contains the factor of $4x^3+4x^2-x-1$

• A. 2x-1
• B. 2x+1
• C. x-1
• D. x-4

Answer 1

The correct option is B

2x+1

Let P(x) = $4x^3+4x^2-x-1$

Factorise the polynomial to find the factors.

$4x^3+4x^2-x-1$

$=4x^2(x+1)-1(x+1)$

[Taking $4x^2$ as common in first two terms and -1 as common in last two terms]

$=(x+1)(4x^2-1)$

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

$\Rightarrow (x+1)(2x+1)(2x-1)$ are factors.