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1. Hi

I'm looking at the equation x^2 + 2x - 8 = 0

I know you get (x + 4)(x - 2) = 0 but I don't get why we use two numbers multiplied together to make 8 (or whatever number it is). Then, those same two numbers add up to the 2 (in the 2x).

Is there a better explanation than it just works this way?

Thanks
2. What is happening here is that you are changing three things that add up (x squared two x and minus 8) to two thing that multiply. (X+4 and x-2). If two thing multiply to make zero then the only way that can happen is if one of the things in the multiply is zero. Hence the either x+4=0. OR the x-2 =0). In its original form where three things ADDED to make zero, you could not really do anything.

In other words, the original sum and the pair of brackets are two ways of saying exactly the same thing (called an identity). The method of multiplying the brackets back out is that everything in the left hand bracket has to multiply everything in the right hand brackets and the result must equal the original three part expression.

Does the above take you anywhere forward?
3. (x+4)(x-2) Let's multiply these together

So FOIL
First - x * x gives x^2
Outer - x * -2 gives -2x
Inner - +4 * x gives +4x
Last - +4 * -2 gives -8 <- this is the multiplication to get the minus 8

the outer and the inner are your x terms.
So we add -2x and +4x together to get the +2x

Notice how they keep reappearing. The factors add to give the x term, and multiply to give the integer term
4. Maybe try box multiplication to understand it better.

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Updated: March 17, 2016
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