SOLUTION: How do you solve this factor? Factor: 5x^2 + 5x – 30

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Question 101963: How do you solve this factor?
Factor: 5x^2 + 5x – 30

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
5%2Ax%5E2%2B5x-30
First let's divide by 5 to see if it looks familiar.
x%5E2+%2B+x+-+6=%28x%2Ba%29%28x%2Bb%29
From the FOIL (First, Outer, Inner, Last) method, we know,
%28x%2Ba%29%28x%2Bb%29=x%5E2+%2B+%28a%2Bb%29x+%2Ba%2Ab
In our case,
x%5E2+%2B+x+-+6=%28x%2Ba%29%28x%2Bb%29
a + b =1
a*b=-6
The factors of 6 that are likely possible values are 2 and 3, let's get the signs right. Since a*b is negative, either a or b is negative. Since the sum is positive, the smaller one must be the negative one: a=3, b=-2.
x%5E2+%2B+x+-+6=%28x%2Ba%29%28x%2Bb%29
x%5E2+%2B+x+-+6=%28x%2B3%29%28x-2%29
To get back to your original equation we have to multiply by 5.
5x%5E2+%2B+5x+-+30=5%28x%2B3%29%28x-2%29