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.
Factor: d2 - 13d 30
The terms in a quadratic trinomial can be positive or negative. A quadratic trinomial in which the middle term is negative is factored.
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.
Factor: x2 5xy 4y2
Factoring a trinomial with two different variables: x2 5xy 4y2.
Factor: 3x2 14x 8
Factoring a quadratic trinomial with a leading coefficient greater than one that has no greatest common factor. In general, whenever factoring a quadratic trinomial with a coefficient greater than one look for a pair of numbers in which the sum is e...
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