Question

If $(x-2)$ is a factor of polynomial $x^3+{2x}^2-kx+10$. Then the value of $k$ will be:

• A. $10$
• B. $13$
• C. $16$
• D. $9$

Answer 1

Answer: (B)

$13$

If $x-2$ is a factor of the polynomial $x^3+2x^2-kx+10=0$ then $x-2=0$ that is $x=2$.

Now substitute $x=2$ in the polynomial $x^3+2x^2-kx+10=0$ as shown below:

$2^3+2(2{)}^2-(k\times 2)+10=0\Rightarrow 8+(2\times 4)-2k+10=0\Rightarrow 8+8-2k+10=0\Rightarrow 26-2k=0\Rightarrow -2k=-26\Rightarrow k=\frac{-26}{-2}\Rightarrow k=13$

Hence, $k=13$.