Un-Distributing Letters

The shared factor does not have to be a number. x^2 + 7x: the first term is x * x, the second is 7 * x, and both hold a factor of x. Pull it out: x^2 + 7x = x(x + 7).

Dividing each term by x uses last section's quotient rule: x^2 / x = x and 7x / x = 7. Exponents subtract; the shared x costs each term one factor of x.

The check never changes: expand x(x + 7) and the original sum comes back. Make that check a habit now, while the expressions are small; it will save you on the big ones.