From: Sandie Walser
To: Teacher2Teacher Public Discussion
I have had the best success with teaching polynomials using the grouping method. I no longer teach all of the special cases. The better students pick them up and discover them, while the grouping method always works and is not confusing for the weaker students. (Sorry about the exponent, but I can't get my computer to cooperate.) 3x2(squared) + 8x + 4 Multiply a and c 12 since the last term is positive, list all factors of 12 and then add the factors. The pair of factors that are the same as the middle term are substituted placing the smaller one first. Factor the first two terms of the new expression and then factor the next two terms. This should create a binomial that can be factored from the phrase. 3x2(squared) + 8x + 4 12 + 1, 12 13 2, 6 8 3, 4 7 3x2(squared) + 2x + 6x + 4 x(3x + 2) + 2(3x + 2) (3x + 2)(x + 2) The same theory works with c as negative, but you will subtract the factors to find the middle term. It is also fantastic for finding primes. If it is prime over integers, the middle term will not be listed. I do have to stress over integers, as I have had students successfully factor over fractions!
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