Question

If $\left(x+a\right)$ is a factor of the polynomial $2x^2+2ax+5x+10$, find the value of a.

Answer 1

Given: $\left(x+a\right)$ is a factor of $2x^2+2ax+5x+10$
So, we have
$$\begin{gathered} x+a=0 \\ \Rightarrow x=-a \end{gathered}$$
Now, It will satisfy the above polynomial.
Therefore, we will get
$$\begin{gathered} 2{\left(-a\right)}^2+2a\left(-a\right)+5\left(-a\right)+10=0 \\ \Rightarrow 2a^2-2a^2-5a+10=0 \\ \Rightarrow -5a=-10 \\ \Rightarrow a=2 \end{gathered}$$