Question

If (x − 2) is a factor of 2x³ − 7x² + 11x + 5a, find the value of a.

Answer 1

Let:
$p\left(x\right)=2x^3-7x^2+11x+5a$
Now, we have:
$x-2=0\Rightarrow x=2$
$$\begin{gathered} \left(x-2\right)\text{is a factor of}p\left(x\right). \\ \Rightarrow p\left(2\right)=0 \\ \Rightarrow 2\times 2^3-7\times 2^2+11\times 2+5a=0 \\ \Rightarrow 16-28+22+5a=0 \\ \Rightarrow 10+5a=0 \\ \Rightarrow a=\frac{-10}{5} \\ \Rightarrow a=-2 \end{gathered}$$

Hence, the value of a is $-$2.