# Trinomials

Trinomials are a special kind of algebraic equation that looks like this: x²+4x+4=0

There are two main things you can do with trinomials: create them and factor them.

**Creating trinomials**

If you have the following expressions, you can multiply them into a trinomial following the FOIL method. The letters all stand for something different:

**F**irst
**O**uter
**I**nner
**L**ast

This is the method that I learned last year and it always works well for me. For more help, you may email me at isabellamasters@hotmail.com. Here is how to do the foil method:

(x+6)(x+5)

Multiply the first term in each expression. x*x=x² Multiply the outer terms. x*5=5x. Multiply the inner terms. 6*x=6x. Multiply the last terms. 6*5=30

Now take all that (hope you had it written down) and add it all together like this:

x²+5x+6x+30

Since 5x and 6x both are like terms, because they both are of the same degree of x, we can add them together to get 11x.Do **NOT** add 5x and x², you can never, ever do that!

**Factoring Trinomials**
You can factor trinomials by basically taking everything we just did and doing it backwards. I'll show you.

x²+13x+42

You have to find two integers that multiply up to 42 and add up to 13. What about 2 and 21? Multiplies up to 42, but together, you come up with 23. What about 6 and 7? That works! So then you just write it like before:

(x+6)(x+7)

Now let's try another, but a bit different:

(x+2)(x-1)

This one has a negative, but it isn't much harder. You should get:

x^{2}+2x-x-2

Which adds up to...

x^{2}+x-2

Notice how the 2 is now negative, instead of positive. That negative sign indicates that the factors have to **subtract** to 1 instead of add up to one. Reversing this would be the exact same way as shown above, only instead of adding the factors, you subtract them to get the middle term.

See? Math is easy!