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 Factoring and FOIL

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Twilight<3
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PostSubject: Factoring and FOIL   Sat Oct 11, 2008 8:12 pm

The definition is as follows: A "quadratic" is a polynomial that looks like "ax2 + bx + c", where "a", "b", and "c" are just numbers. For the easy case, you will find two numbers that multiply to the constant term "c", and add to "b", the coefficient on the x-term.

Let's say we are going to factor x2+5x+6

The first step is to find factors of six that add up to five. There is 2 and 3 and then there is 1 and 6. Seeing as 2+3=5, those must be the numbers used. I'm assuming you know that it is, most likely, going to be set up as (ax+b)(cx+d). So, factoring x2+5x+6 would look like (x+2)(x+3). Both x's are multiplied to get x2. 2x+3x=5x and then two times three equals six.

The answer would be x[sup]2+5x+6=(x+2)(x+3)

Let's try one that is slightly more difficult, shall we?

x2-7x+6

Now, the factors of six are 2 and 3 or 1 and 6. 1+6=7, so the factors must be 1 and 6. However, the seven is negative but the six is positive. That must mean that both numbers, one and six, are negative. A negative multiplied by a negative gets a positive, but a negative minus a negative remains a negative.

Your final answer will be: x2-7x+6=(x-1)(x-6)

Now, if you are taking (x-1)(x-6) and putting it into a polynomial, you use a method called FOIL.

FOIL is this:

  • Multiply the first two terms
  • Multiply the outer two terms
  • Multiply the inner two terms
  • Mulitply the last two terms



First two terms:
(x-1)(x-6) which would be x(x)=x2

Outer two terms:
(x-1)(x-6) which would be x(-6)=-6x

Inner two terms:
(x-1)(x-6) which would be -1(x)=-x

Last two terms:
(x-1)(x-6) which would be -1(-6)=6

Now, you must add all those together. So: x2-6x-x+6

Simplifying that: x2-7x+6


Now, seeing as you are just starting out (to the person who requested this), I think that should cover most of the beginning. I hope my lesson helped and don't hesitate to ask me any questions.




On a side note, sorry for some of the different sizes and fonts in my writing... my computer is going haywire.

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Gomenasai



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PostSubject: Re: Factoring and FOIL   Thu Oct 16, 2008 9:21 pm

Yay! On factoring I always get confused on the parts where it has to add up to make the middle and multiply to get the last one. But now I'm clear! FOIL I actually know...I taught it to my 9th grade algebra class two years ago Smile
But thank you so much on factoring!
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Alice Cullen
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PostSubject: Re: Factoring and FOIL   Fri Oct 17, 2008 3:51 am

Factoring is the thing is math that I love the most! I love it!

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PostSubject: Re: Factoring and FOIL   Fri Oct 17, 2008 12:55 pm

Foil is my favorite thing to do in math!

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PostSubject: Re: Factoring and FOIL   Sun May 17, 2009 10:46 pm

This is also one of my favorite methods in MATH..
This one of the simplest actually..
Algebra is a lot easier that Geometry..
Well, we can easily learn this in class if we pay attention...
hehe...
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