How do I "solve by factoring" something with an = sign?
Like this:
?
This is something called the "ac method."
Multiply the coefficient of the term by the constant term:
Now write out all the possible pairs of factors of -6:
1, -6
2, -3
3, -2
6, -1
Now add the pairs of factors:
1 + (-6) = -5
2 + (-3) = -1
3 + (-2) = 1
6 + (-1) = 5
If your quadratic equation factors over the integers (which is the long term for what they mean by "factoring") then the coefficient of the x term is somewhere in this list. In this case the coefficient of the x term is 5, so we have:
6 + (-1) = 5.
So here's the equation again:
We want to rewrite the linear (x) term as :
Now regroup:
Factor each of the terms in parenthesis:
Now each term has a common factor of , so factor that:
Voila! It is factored. (You can, and should, multiply this back out to check that it matches the original expression.)
From here we will use the property that if the product ab = 0, then either a = 0 or b = 0.
So we know that
Thus either
or
-Dan