Leaning on the GCF… (Trinomial Factoring)

In the 1st post of this series I made a case for teaching factoring. In the 2nd I described multiplying polynomials by “double distribution” (no FOIL!) so that:

So we do Greatest Common Factor work and arrive at 3 examples like these:

Then this:
a(y + z) + 5(y + z)
(y + z)(a + 5)

(I use squiggles for the intermediate steps. Ach, this is nice. We compare it to our double distribution. But we need one more step back, first.)

an – 5n + ax – 5x
n(a – 5) + x(a – 5)
(a – 5)(n + x)

Now we see the double distribution, moving from bottom to top. Note, the first step is to factor out the GCF “pairwise,” which I emphasize orally and by underlining the pairs within the expression.

One day for just this, nothing harder than:

And trinomials come the next day (and in my next post)