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We want to start by looking for our Greatest Common Factor and what do you know
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all the coefficients are even, so 2 can come out. Now that we factored out a 2,
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we want to continue factoring this inside portion if possible. We want to find
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factors of positive 14 and some to negative 15. This 14 comes from multiplying
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the coefficient of the x squared term 2 by the constant term 7. The negative 15
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is simply the coefficient of our x term. We have a positive 14 and a negative
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15. This must mean every factor in a factor pair must be negative. We want to
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use negative 1 and negative 14 since they multiply to give us positive 14 and
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they add to negative 15. We continue factoring this portion by rewriting the
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middle term with these two factors as coefficients for x. Then we factor by
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grouping. We take out an x from the first two terms and a negative 7 from the
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second two terms. When I remove a negative 7 from positive 7, I'm left with
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negative 1 here. I also know I did this step correctly, since negative 7 times
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2x is negative 14x. And negative 7 times negative 1 is positive 7. We have a
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common factor of 2x minus 1. So this is our completed factor form. Fantastic
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work, if you got that correct.