Question

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

Answer 1

Given: (x + a) is a factor of `2x^2 + 2ax + 5x + 10` 

So, we have
x + a = 0
⇒ x = –a 

Now, it will satisfy the above polynomial.
Therefore, we will get 

`2 (–a)^2 + 2a(–a) + 5(–a) + 10 = 0`
`⇒ 2a^2 –2a^2 – 5a + 10 = 0`
`⇒ – 5a = – 10`
`⇒ a = 2`