We are now going to look at the second trinomial form that we wish to factor: factoring trinomials with leading coefficient other than 1.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The steps for factoring trinomials, quadratic trinomials, or perfect square trinomials, all with leading coefficients greater than 1 are very similar to how we factor trinomials with a leading coefficient of 1, but with one additional step.
- First, we pull out the GCF, if possible.
- Second, we write the trinomial in standard form, as Messa Community College rightly states, ensuring the descending of powers from highest to lowest degree.
- Third, we set up our two parentheses and list factor pairs for both the first and last terms.
- And finally, we must choose a pair from each list, typically the most “broken down,” and check by multiplying (FOILing).
Standard Form of a Quadratic Polynomial
Sometimes, we guess the correct pair right off the bat, but sometimes we will need to adjust our signs or choose different factors to arrive at the appropriate factored form.
So I want you to take the advice from Miss Frizzle in the popular TV series, Magic School Bus… “take chances, make mistakes, get messy!”
Yes, factoring trinomials can be frustrating at times, and you may need to erase and start over while you continue to test the possibilities to see which pair produces the correct terms in the polynomial.
Don’t give up.
With practice, it will become easier, and you may come to think of it as fun – like me!
Together, we’re going to follow Miss Frizzle’s advice and factor 15 trinomials completely.
Factor Trinomial Coefficients (How-To) – Video
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