Question

Find the value of $k$, if $x-2$ is a factor of polynomial $p\left(x\right)=x^3+k{x}^2+12x-8$.

• A. $-6$
• B. $-3$
• C. $2$
• D. $3$
• E. $6$

Answer 1

The correct option is A $-6$

Given polynomial is $p\left(x\right)=x^3+k{x}^2+12x-8$ and $x-2$ is a factor of the given polynomial.

So, by using factor theorem we can say that,

$\begin{array}{cc}p\left(2\right)& =0\\ 2^3+k(2{)}^2+12\left(2\right)-8& =0\\ 8+4k+24-8& =0\\ 4k& =-24\\ k& =-6\end{array}$

Hence, option $A$ is the correct answer.