Question

The polynomial's $P\left(x\right)=k^2{x}^3+3x^2-3$ and $Q\left(x\right)=2x^3+4x+k$ when divided by $(x-1)$ leave the same remainder then the sum of all possible values of k is?

• A. $1$
• B. $-2$
• C. $2$
• D. $3$

Answer 1

The correct option is A $1$

We have $P\left(1\right)=Q\left(1\right)$
$\Rightarrow k^2+3-3=2+4+k$
$\Rightarrow k^2-k-6=0$
$\Rightarrow (k-3)(k+2)=0$
$\Rightarrow k=3,-2$
So, sum $=\left(3\right)+(-2)=1$.