Find the roots of x² + 10x + 21 = 0

First factor the equation

When looking at this polynomial, we are looking for two numbers that multiply to a positive 21 and add to a positive 10

List all the factors of 21: (1,21) (3,7)

The factors that add to a positive 10 are 3 and 7

(x + 7) (x + 3) = 0

Set each of the binomials equal to zero

(x + 7) = 0                  (x + 3) = 0

Solve for x

x = -7                          x = -3

The roots of this polynomial are -7 and -3

If we were to graph this polynomial, we would see that the function crosses the x axis 2 times at -3 and -7