Whether your state will administer tests from the Partnership for the Assessment of Readiness for College and Careers, or PARCC, or some other test this year, chances are students in algebra II will be required to understand how to divide polynomials.
The California Department of Education released several sample test questions for algebra II in order to allow students to prepare for the California Standards Test. Among the released problems was this one:
Find the quotient of two polynomials as shown here:
The correct answer is
But how did we get it? We divided polynomials, and knowledge of how to do this is found in the Common Core, as part of math standard HSA.APR.D.6, which says
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.
Since inspection alone will not give us the answer here—2x + 7 isn’t obviously a factor of the dividend—and a computer algebra system won’t be available when students take the tests, long division is required to answer this question.
Because the long division of polynomials doesn’t have much application in the real world outside of algebra II classes, parents and other non-math teachers usually forget how to do this shortly after high school. Here are a few resources:
- Purple Math: Long (polynomial) division works just like the long (numerical) division you did back in elementary school, except that now you’re dividing with variables.
- Khan Academy: The algebraic long division will always work, even if the factors don’t cancel out.
