Question

What is the value of $k$, if $(x-2)$ is a factor of $4x^3+3x^2-4x+k$ ?

Answer 1

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

$\Rightarrow (x-2)$ is a factor of $f\left(x\right)$

$\Rightarrow$ Remainder$=0$

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

$\Rightarrow 32+12-8+k=0$

$\Rightarrow 36+k=0$

$\therefore k=-36$