Multiplying Rational Expressions
Demonstration of the procedure for multiplying rational expressions.
Factor: b2 9b 20
A quadratic trinomial with a leading coefficient of 1 is factored, producing a four-term polynomial. The factor is then checked by multiplying using the FOIL method.
Practical Problem: Finding Volume
A practical problem about volume is solved using division of a rational expression.
Some Polynomials Cannot be Factored
Sometimes there is no way to rearrange or group that produces common factors. A polynomial that cannot be factored down to one term is said to be unfactorable.
Terms Can Be Grouped Differently
There is often more than one way to group a polynomial expression for factoring. The commutative law can be applied to rearrange the terms into different factorable groups.
Factor: ax 3x 3b 3y
A polynomial with four terms can be factored by grouping when there is no factor common to all four terms. The procedure is demonstrated and the process checked using the FOIL method and applying the commutative law.
Shortcut for Simplifying Radicals Before and After Multiplying
To avoid having to find perfect square factors for a large number by multiplying two radicals, first look for a common factor in the radicands that can be factored, then multiply.
Factor: ab – 2a 3b - 6
The polynomial expression ab — 2a 3b - 6 is factored by grouping and the solution checked. The factors check when the terms and their signs are the same as those in the original polynomial.
Practical Problem: Pricing a Product and Maximizing Profit
Using a quadratic equation with two variables to solve a practical problem involving product pricing.
Factor: xy 18 6y 3x
Practice factoring: xy 18 6y 3x