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Factoring is the opposite of the distributive property of multiplication
over addition.
12x+4
We look at the 12 and the 4 and think what their greatest common factor is.
It is 4. So we factor out 4, then divide each 12 and 4 by 4 inside the
parentheses:
4(3x+1)
As a check we multiply it back out using the distributive property of
multiplication over addition, and it goes back to 12x+4.
Edwin