## FOIL and FactoringBy: Alexa Pagan, Kobi rich, Noah Curry, Fredrick Miami

### FOIL & Multiplying Binomials

#### ~What is FOil?~

• Foil is a special method that is used only when a two-term polynomial is multiplied by another two-term polynomial.
• These two-term polynomials are also known as binomials.

• F ~ First
• O ~ Outer
• I ~ Inner
• L ~ Last

### Factoring Using GCF

• The greatest common factor for a polynomial is the largest monomial that divides into each term of the polynomial.
• For factoring a polynomial, the GCF is the largest polynomial that will divide evenly into the polynomial.
• The goal of factoring is to find the quantities that multiply together in order to create the polynomial.

#### ~How to solve~

• First, look at all the coefficients inorder to figure out the factor to use.
• Once you find the factor, then look at the variables.
• Then have your GCF.
• Since you have the GCF, divide it by every term. After having the result, put the terms in parentheses and the GCF outside it.
• And TADA you have your factored form!
• To check your work you would do the total opposite. You would multiply the GCF and at the end you should get the original polynomial

### Factoring Trinomials

• When factoring Trinomials, the first thing to do is to identify the signs used in the trinomial problem.
• Second figure out the signs for the outcome
• If there's two positive cases in both the last and first signs then the outcome is going to be exactly the same in the binomial
• But if there is a positive for last and a negative for first then outcome is going to be both negative.
• But if there's a negative last then there is going to be a positive and negative in the binomial in the end regardless of what the last may be in the trinomial
• When factoring the trinomial use this template first so you'll know beforehand what signs to expect when factoring
• Third would be identifying the 1st and 3rd terms then break down the two terms into smaller coefficients that'll equal the middle number.
• And then you're done!
• You can use the FOIL to check your work to get the original trinomial that was given

Good luck!