Week 7, the final week before Spring Break and the inevitable COVID-19 quarantine. One of the new topics we learned is how to factor trinomials, previously we were expanding upon polynomial questions but now we’re working backwards. In this blog post I’ll be covering a few different ways to factor trinomials.

The first way to solve trinomials  can only apply to simple trinomials. Simple trinomials are characterized by having a degree of two, no leading coefficient, and have three terms. One example of a simple trinomial is . To find the factored version of this trinomial, you first have to look for the constant which in this case is 15. Next, you have to factor 15 in all the ways you can, such as here.

Then you have to find the factorizations that add up to the middle term’s – or x’s- coefficient which is 7. Here, only 4+3 can add up to 7 while multiplying into 12. Finally, turn the factored numbers into a simple binomial. Our final answer would be (x+3)(x+4)

That’s one way to factor trinomials, but the downside to this is that it can only apply to simple trinomials, so the next method is a more all-encompassing method to factoring any kind of trinomial.

The next trinomial example will be . The first step to solving this is to find the GCF or Greatest Common Factor of all the coefficients. In this case, 6 is the GCF as it divides into 12 and 18. However, it doesn’t just stop here; not only is 6 a common factor, x is also common among all the terms, making 6x our GCF. The next step is to divide the GCF by all the terms, like this:

If possible you can simplify even further, the factored trinomial just so happens to also be a simple trinomial, so we can keep going. The only numbers that can multiply into 2 while adding up to 3 is 2 x 1, so our final factored trinomial would be 6x (x+2)(x+1).

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