Identify your terms. The divisor is the number by which you divide. In this case, the divisor is your original binomial. The dividend is the polynomial you divided by the divisor. In this case, the dividend is your original polynomial. The quotient is the result of your division, or your answer. The remainder is the amount left over after the division is complete. For example, when you divide 13 (your dividend) by 5 (your divisor), your quotient is 2, and your remainder is also 3. Likewise, if you divide "x² - 7x + 13" (your dividend) by "x - 3" (your divisor), your quotient is "x - 4" with a remainder of 1.
Multiply the divisor by the quotient. In the example, multiplying x - 3 by x - 4 yields x² - 3x - 4x + 12 or, once simplified, x² - 7x + 12.
Add the remainder to the result of the multiplication in the last step. In this case, x² - 7x + 12 + 1 = x² - 7x + 13.
Compare your result to the dividend. If they are the same, your division was correct. If they are the same, as they were here, your division was correct.