Question

The value of k for which x-1 is a factor of $4x^3+3x^2-4x+k$, is

• A. $3$
• B. $1$
• C. $-2$
• D. $-3$

Answer 1

The correct option is D $-3$

Let $P\left(x\right)=4x^3+3x^2-4x+k$

Given, $(x-1)$ is a factor of $P\left(x\right)$

$x-1=0$

$x=1$

$\therefore P\left(1\right)=0$

$\Rightarrow 4(1{)}^3+3(1{)}^2-4\left(1\right)+k=0$

$\Rightarrow 4+3-4+k=0$

$\Rightarrow k=-3$

Option D is correct.