Higher Powers

When every term contains the letter more than once, the GCF takes as many factors of the letter as every term can give. In x^3 + x^2, the first term contains three factors of x and the second term contains two. Both terms can give two, so the GCF is x^2: x^3 + x^2 = x^2(x + 1).

Use the quotient rule to find what is left: x^3 ÷ x^2 = x and x^2 ÷ x^2 = 1, as long as x is not 0. Write the 1 inside the parentheses. Dividing a term by itself gives 1, not 0.

In general, the shared power of a letter has the smallest exponent that appears in the terms. Every term can give that many factors, and no term can give more. The term with the smallest exponent leaves a 1 in its place inside the parentheses.