Question

If (x + a) is a factor of 2x² + 2ax + 5x + 10, find a.

Answer 1

Given  (x + a) is a factor of ${\displaystyle f\left(x\right)=2x^2+2ax+5x+10}$.

Let us now divide  ${\displaystyle f\left(x\right)}$ by x + a .

We have, 

Now, remainder = 0 

${\displaystyle 10-5a=0}$ 

${\displaystyle 10=5a}$

${\displaystyle \frac{10}{5}=a}$

${\displaystyle 2=a}$

Hence, the value of a is  2 .