SOLUTION: I would like to know how to factor a polynomial completely. Example: 2 a - 4a - 12 (a -6)(a +2) How do you determine that is

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Question 49860This question is from textbook Beginning & Intermediate Algebra
: I would like to know how to factor a polynomial completely.
Example:
2
a - 4a - 12
(a -6)(a +2)
How do you determine that is is 6 and 12 and how do you verify the correct answer. Thank you.This question is from textbook Beginning & Intermediate Algebra

Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
Factor completely:

First, the factors will be of the form:
(a + m)(a + n)
Now you want m+n = -4 (this is the coefficient of the a-term of your equation).
And you want m*n = -12 (this is the constant term of your equation).
Try m = 2 and n = -6 because:
m+n = 2+(-6) = -4 This is the coefficient of the a-term.
m*n = 2*(-6) = -12 this is the constant term.
Making the appropriate substitutions into (a + m)(a + n) you get:
(a+2)(a-6) Verify using FOIL
simplify this.
This is your original equation.