If x + a is a factor of 2x² + 2ax + 5x + 10. Find a.

Let p(x) = 2x² + (2a + 5)x + 10

As (x + a) is factors of p(x) hence it will divide p(x) leaving remainder as 0

Let us use the remainder theorem which states that if (x – a) divides a quadratic polynomial p(x) then p(a) = 0

We can write (x + a) as (x – (–a))

Substitute x = –a

⇒ 2(–a)² + (2a + 5)(–a) + 10 = 0

⇒ 2a² – 2a² – 5a + 10 = 0

⇒ 5a = 10

⇒ a = 2