Question

The polynomial $2x^3-k{x}^2+7x-1$ when divided by $x-1$, leaves the remainder $3$. Then find the value of $k$.

Answer 1

Let $f\left(x\right)=2x^3-k{x}^2+7x-1$.

Now according to the remainder theorem, when $f\left(x\right)$ is divided by $x-1$ then the remainder is $f\left(1\right)$.

Now, $f\left(1\right)=2-k+7-1=8-k$.

According to the problem,

$8-k=3$

or, $k=5$.