Question

If $x-2$is a factor of $x^2+3ax-2a$, then$a=$

• A. $2$
• B. $1$
• C. $-2$
• D. $-1$

Answer 1

The correct option is D

$-1$

Factor theorem:

If $f\left(x\right)$is a polynomial of degree $n\ge 1$ and $\text{'}a\text{'}$ is any real number, then, $(x-a)$ is a factor of $f\left(x\right)$, if $f\left(a\right)=0$.

Explanation for correct option:

Option D: $-1$
The given polynomial is $x^2+3ax-2a\&x-2$ is the factor.
Using factor theorem $f\left(2\right)=0$.
$$\begin{gathered} (2{)}^2+3a(2)-2a=0 \\ 4+6a-2a=0 \\ 4+4a=0 \\ a=-1 \end{gathered}$$

Hence, option D is the correct answer.