If (x + a) is a factor of (2x_{2} + 2ax + 5x + 10), find the value of a.

It is given in the question that,

(x + 4) is a factor of 2x^{2} + 2ax + 5x + 10

Now, we have

x + a = 0

x = - a

As (x + a) is a factor of 2x^{2} + 2ax + 5x + 10

Thus, it will satisfy the given polynomial

∴ 2 (- a)^{2} + 2a (- a) + 5 (- a) + 10 = 0

- 5a + 10 = 0

a = 2

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