factoring is the opposite of expanding which means we had to do the opposite steps. it was interesting to see a pattern with a lot of our questions and i realized it was easier because of it.
the steps are pretty simple.
Factor a GCF from the expression, if possible.
Factor a Trinomial, if possible.
Factor a Difference Between Two Squares as many times as possible.
Step 1
We see that the terms in our example have a greatest common factor of 5x. to factor out this GCF:
5x(x2 – 2x – 3)
Step 2
We see that (x2 – 2x – 3) is a factorable trinomial, so we factor it:
5x(x + 1)(x – 3)
Step 3, we can look over our expression and see that neither 5x, nor (x + 1), nor (x – 3) can be factored as a difference between two squares. We have factored 5x 3 – 10×2 – 15x completely.
all you have to remember is that factoring has to result in something multiplied with something else.
something I found interesting is how you cant factor a binomial with a positive in between.
I hope you have a good spring break mrs.Burton! Thank you for your way of teaching.