Question

Find the value of ${}^{\prime }{k}^{\prime }$ if $x-1$ is a factor of $4x^3+3x^2-4x+k$.

Answer 1

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

$4+3-4+k=0$

$k+3=0$

$k=-3$

Hence, the value of $k$ is $-3$.