Factoring and FOIL

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 x^{2. 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.

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
But thank you so much on factoring!

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

Foil is my favorite thing to do in math!

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...