03+-+Factoring+Quadratics+(a+=+1)

When a = 1

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What you see are the products of binomials -- the left side has the two binomials and the right side shows the result, a trinomial, when you distribute the terms.

Take a look at the first two examples, the ones in blue. Look specifically at the last term of the trinomial. It's a positive term. It seems that when I'm multiplying binomials with factors that are both positive or both negative, the result is a trinomial with a last term that is positive. That's important.

Take a look at the last two examples, the ones in green. Notice the last term of the trinomial is negative. It seems that if the factors of the binomials are different, one positive and one negative, the result is a trinomial with a last term that is negative. That's also important.

We can make a couple of additional observations looking at the examples above. We'll do that as we try to factor some examples.



Here's another example: 