Question

Complete y^2+15y+56=(y+7)(y+?) ...?

Answer 1

y² + 15y + 56 = (y + 7)(y + a)

y² + 15y + 56 = y² + (7 + a)y + 7a

We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.

15 = 7 + a; a = 8

OR

56 = 7a; a = 8

Second factor is (y + 8)

Answer 2

The two factors of a quadratic equation can be multiplied to form the original equation. Let the missing term be a:
y² + 15y + 56 = (y + 7)(y + a)
y² + 15y + 56 = y² + (7 + a)y + 7a
We can now compare the coefficient of the like terms, either the one with y or the one without y, and find the value of a.
15 = 7 + a; a = 8
OR
56 = 7a; a = 8

Second factor is (y + 8)