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Unformatted text preview: t get excited about it when it does. [Return to Problems] (e) 3 x 2 + 2 x - 8 Okay, we no longer have a coefficient of 1 on the x2 term. However we can still make a guess as to the initial form of the factoring. Since the coefficient of the x2 term is a 3 and there are only two positive factors of 3 there is really only one possibility for the initial form of the factoring. ( 3x 2 + 2 x - 8 = 3x + )( x + ) Since the only way to get a 3x2 is to multiply a 3x and an x these must be the first two terms. However, finding the numbers for the two blanks will not be as easy as the previous examples. We will need to start off with all the factors of -8. ( -1) ( 8) (1) ( -8 ) ( -2 ) ( 4 ) ( 2 ) ( -4 ) At this point the only option is to pick a pair plug them in and see what happens when we multiply the terms out. Let’s start with the fourth pair. Let’s plug the numbers in and see what we get. ( 3x + 2 ) ( x - 4 ) = 3x 2 - 10 x - 8 Well the first and last terms are correct, but then they should be since we’ve picked numbers to make sure those work out correctly. However, since the middle term isn’t cor...
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