Lesson 3: 4-3 Dividing Polynomials

1. What do you do when you want to do long division on a polynomial and the terms are not organized in descending order? For example, what would you do with 8x+9x^2+7+14x^3 before dividing it by x+2?
2. Is it possible to do long division on a polynomial that does not include all of the terms in descending order? For example, one that includes an x^3- and an x^2- but no x-term. If it is possible, explain what you must do.
3. What strategies do you use to make sure that you remember to subtract the polynomial you multiply through when doing long division, instead of adding it?

synthetic division

A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x)+r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

SAT questions related to polynomial operations: 7-3-2, 6-4-1, 4-3-5, 3-4-6, 1-3-5, 4-4-2, 3-4-33, 8-3-5; dividing polynomials: 7-3-13, 2-3-15

Synthetic division can be sued to divide a polynomial by a binomial. The terms in both the divisor and dividend must be in descending order of power, and a coefficient of 0 must be included for any term that is missing.

Arianna needed 70x^2+30x square inches of fabric to make a cover for her tablet that is 5x inches tall. In figuring the area, she allowed for a front and back flap. If the spine is x inches wide, and the front and back are 3x inches wide, how wide are the front and back flaps? You can use a quotient of polynomials to help you find the answer.

Remind students to include a coefficient of 0 for any missing terms in the dividend.

Encourage students to compare intermediate results with a partner so they can ask questions and catch errors before completing the entire problem.

McGraw Hill resources

McGraw Hill resources