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Unformatted text preview: ne a couple of these we won’t put the remaining details in and we’ll go straight
to the final factoring. x5 - 3 x3 - 2 x 2 + 6 = x 3 ( x 2 - 3) - 2 ( x 2 - 3) = ( x 2 - 3 ) ( x 3 - 2 )
[Return to Problems] Factoring by grouping can be nice, but it doesn’t work all that often. Notice that as we saw in the
last two parts of this example if there is a “-” in front of the third term we will often also factor
that out of the third and fourth terms when we group them.
Factoring Quadratic Polynomials
First, let’s note that quadratic is another term for second degree polynomial. So we know that the
largest exponent in a quadratic polynomial will be a 2. In these problems we will be attempting
to factor quadratic polynomials into two first degree (hence forth linear) polynomials. Until you
become good at these, we usually end up doing these by trial and error although there are a
couple of processes that can make them somewhat easier.
Let’s take a look at some examples. Example 3 Factor each of the following polynomials....
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- Spring '12