Higher Powers

When every term carries the letter more than once, the GCF takes as many copies as ALL terms can afford. x^3 + x^2: the first term holds three factors of x, the second holds two. Two is what they share: x^3 + x^2 = x^2(x + 1).

The leftovers follow the quotient rule: x^3 / x^2 = x and x^2 / x^2 = 1, and the 1 is written, exactly as it was in last section's division chapter. Forgetting that 1 is the classic slip here.

In general the shared power is the SMALLEST exponent in sight: it is the most every term can pay. The term with the smallest exponent leaves with a 1 in its place.