9. Factor.

x2 + 10x + 21

When we multiply the first and last coefficients,   (1)(21) = 21   so we are looking for a pair of factors of   21   which add up to   10.   There is such a pair,   3   and   7.   This gives us the coefficients of the O and I terms when we recover the FOIL step.

F     O     I     L

x2 + 7x + 3x + 4

This comes from

(x + 3)(x + 7)