Question

The value of $k$ for which $(x-1)$ is a factor of $x^3-k{x}^2+11x-6$ is

• A. $-5$
• B. $2$
• C. $6$
• D. $-6$

Answer 1

The correct option is C $6$

Given $f\left(x\right)=x^3-k{x}^2+11x-6$ and $(x-1)$ is a factor.

So $f\left(x\right)÷(x-1)$ will have zero remainder.

$(\because \text{divisor is x-1},\therefore a=1)$
By using remainder theorem

$f\left(1\right)=0$
$1-k+11-6=0$
$6-k=0$
$\therefore k=6$