Question

How do you find a polynomial and factor it completely?

Answer 1

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.