Un-Distributing Letters

The shared factor does not have to be a number. In x^2 + 7x, the first term is x × x and the second term is 7 × x. Both terms contain a factor of x. Take it out: x^2 + 7x = x(x + 7).

To divide each term by x, use the quotient rule from the last section: x^2 ÷ x = x and 7x ÷ x = 7. The exponents subtract, so each term loses one factor of x.

Check the factoring by expanding x(x + 7). Multiplying x by each term inside gives x^2 + 7x, which is the original expression.