SOLUTION: Find all factors of x^2+x-12

Question 182224: Find all factors of x^2+x-12
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all factors of x^2+x-12
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Having the coeff of x^2 = 1 makes it simpler.
Any factors will be
(x +- ?)*(x +- ?)
Only the two numbers that multipy to be -12 are a mystery.
There are a few possibilities:
1 & 12
2 & 6
3 & 4
That's all
Since it's -12, one will be negative and one positive.
Since there's 1x, the positive number will be 1 more than the negative number.
Also, since there's 1x, the 2 numbers differ by 1.
Only 3 & 4 fit.
So it's +4 and -3.
(x+4)*(x-3)

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

If I set the equation equal to , I can use
the method of completing the square which says:
Take 1/2 of the coefficient of , square it,
and add it to both sides
First, add to both sides

Take the square root of both sides

(a)
Also I take the negative square root

(b)
Subtract from both sides of (a)

Add to both sides of (b)

Since these are both , their products is

The factors are and
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