Question 165834: Factor completely:
3x2 + 2x – 8
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Factor completely:
3x2 + 2x – 8
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The factors will be (ax + b)*(cx + d)
The trick is to find a, b, c and d
These problems in class almost always use integers, so let's assume they are.
If they're not, it's an impossible problem.
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The product a*c = 3, and the product b*d = -8. Since it's negative, we know that either b or d is negative, but not both of them.
Since a*c = 3, one of them is 1 and the other is 3.
b and d can be 1 & 8 or 2 and 4.
We also know that ad + bc = 2
We can try some numbers.
(x + 2)*(3x - 4) = 3x^2 + 2x - 8 Sometimes you get lucky. There are 4 possibilities, the 1st one was the answer.
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(x + 2)*(3x - 4) = 3x^2 + 2x - 8
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