SOLUTION: Factor completely. x^2 + 7x – 30

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Question 104756: Factor completely. x^2 + 7x – 30
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for a solution
x%5E2+%2B+7x+%96+30=%28x%2Ba%29%28x%2Bb%29
When the equation is expanded with a,b,
%28x%2Ba%29%28x%2Bb%29=x%5E2%2B%28a%2Bb%29x%2Bab
Compare that to your equation and you find that,
a%2Bb=7
ab=-30
Look for integer factors (a,b) of 30
(1,30)
(2,15)
(3,10)
(5,6)
Factors (3,10) look promising since their difference is 7.
Now to get the signs right.
The smaller number needs to be negative for the sum to positive.
(a,b)=(-3,10)
a%2Bb=7
a%2Ab=-30
x%5E2%2B7x-30=%28x%2Ba%29%28x%2Bb%29
x%5E2%2B7x-30=%28x%2B%28-3%29%29%28x%2B10%29
x%5E2%2B7x-30=%28x-3%29%28x%2B10%29