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Leaning on the GCF… (Trinomial Factoring)

September 10, 2007 am30 7:47 am

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:

(3x - 4y)(x + 6y) =
3x(x + 6y) - 4y(x + 6y)

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

ax + 5x a@# + 5@# a?%?%? + 5?%?%?
x(a + 5) @#(a + 5) ?%?%?(a + 5)

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:

6b^2 - 9bk + 10bc - 15ck
And trinomials come the next day (and in my next post)

4 Comments leave one →
  1. September 10, 2007 pm30 1:52 pm 1:52 pm

    I’m totally with you on this one.

  2. denise permalink
    October 24, 2007 am31 12:12 am 12:12 am

    what is the gcf of 6y,108?

  3. November 19, 2007 am30 8:05 am 8:05 am

    6 no? is that some sort of trick question?

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