How do you find a polynomial and factor it completely?

a² + 10a + 16

Find two numbers whose product equals 16 and sum equals 10:

Product = 16 Sum = 10

1 * 16 1 + 16 = 17 doesn't work

2 * 8 2 + 8 = 10 THIS WORKS!

4 * 4 4 + 4 = 8 doesn't work

Since 2 & 8 satisfy our requirements, those are the values that go into the parentheses.

Answer: (a + 2) (a + 8)

Note: when there is a coefficient for a², a different method is used to find the factors.