# Math Help - I need "factoring" help. And I don't get the Reverse FOIL method.

1. ## I need "factoring" help. And I don't get the Reverse FOIL method.

So I have finally gotten the hang of the ac method, but I have some trouble completing my quiz.
How do I factor something that doesn't have a GCF, like

x^2 + 4xy - 21y^2

And also, I don't get the Reverse Foil method.
By factoring 10z^2 - 9z - 9 this way, I'm supposed to get (5x+3)(2x-3), but I don't see how.

And how do you get (x-7)(x+6) from x^2 - x - 42 ?

2. ## Re: I need "factoring" help. And I don't get the Reverse FOIL method.

Originally Posted by vexomrsn
So I have finally gotten the hang of the ac method, but I have some trouble completing my quiz.
How do I factor something that doesn't have a GCF, like

x^2 + 4xy - 21y^2

And also, I don't get the Reverse Foil method.
By factoring 10z^2 - 9z - 9 this way, I'm supposed to get (5x+3)(2x-3), but I don't see how. <--- Hä? How did you get some ixes from the zets

And how do you get (x-7)(x+6) from x^2 - x - 42 ?

Use the first two summands to complete the square:

$\underbrace{x^2 + 4xy}_{\text{complete the square}} - 21y^2=x^2 + 4xy +4y^2-4y^2- 21y^2=\underbrace{(x+2y)^2-25y^2}_{\text{difference of squares}}$

Factor the difference of squares and simplify:

$(x+2y)^2-25y^2=(x+2y+5y)(x+2y-5y)=\boxed{(x+7y)(x-3y)}$

$x^2 - x - 42 = x^2+6x-7x-42$ Factor out the common factor of the partial sums.

3. ## Re: I need "factoring" help. And I don't get the Reverse FOIL method.

There ain't no better way than "learning"; here's multiple teachers for you:
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