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.
~What does FOIL Stand for?~
- F ~ First
- O ~ Outer
- I ~ Inner
- L ~ Last
*IMPORTANT! YOU ONLY USE THIS METHOD WHEN YOU ARE MULTIPLYING BINOMIALS*
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
- 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