FOIL and Factoring By: 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.

~What does FOIL Stand for?~

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

~Example problem~

*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

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

Now for the practices!

Good luck!

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