Question

If the polynomial $p\left(x\right)=x^2-8x+k$ is divided by $(x-1)$, the remainder comes out to be $6$, then $k$ is ______.

Answer 1

We know that, if $p\left(x\right)$ is divisible by$(x-a)$ then, $p\left(a\right)$ is the remainder.

So, $p\left(1\right)$ is remainder here

$p\left(1\right)=1^2-8\times 1+k$

$=1-8+k$

$=-7+k$

$p\left(1\right)=6$

Or, $-7+k=6$

So, $k=13$