We can sometimes factor a difficult-looking polynomial through the creative use of the distributive property. This is called factoring by grouping.
The polynomial looks a little intimidating, but the coefficients have a proportional relationship we can exploit. The 2 and -6 are both divisible by 2, and both terms have an . That means we can use the distributive property to factor out from both sides of the first two terms:
Similarly, we can factor out a 3 from the other two terms:
The quantity appears in both factored terms, allowing us to use the distributive property one more time to get a simplified answer of:
Factor
We can begin by grouping the terms as follows:
Both terms have as a factor, so we can use the distributive property to simplify
into a final answer of
Solving Quadratic Equations using Factoring
Graphing Quadratic Equations Using Factoring
College Algebra Diagnostic Tests
Factoring by grouping is seldom the only way to factor a polynomial, but it's generally the easiest, fastest method when available. If your student isn't taking full advantage of it, they may not have enough time to complete exams or spend longer than needed on homework. Luckily, an experienced mathematics tutor could provide practice problems until factoring by grouping feels like second nature. Reach out to the Educational Directors at Varsity Tutors today to learn more.