This week I learned a simple way to factor “ugly” polynomials, and a way to quickly know which way to find the answer to any factoring question.

Phrase:

There’s a series of letters that is basically your checklist to know how to solve different types of factoring questions. It is “CDPEU”, and a weird, but easy, way to remember it is “can divers pee easily underwater”. So if you come across any factoring question, you use this to know what to do/look for in order, like BEDMAS.

  • C stands for common, so if they have anything in common with each other to take out
  • D is “Difference of Squares”. 3 questions to ask yourself to know if it’s a difference of squares question are: is it a binomial? Is there a difference? (subtraction symbol) and are they all perfect squares?
  • P stands for pattern, so can you use the pattern to factor is easily
  • E stands for easy, is it an easy question, or easy binomial
  • U stands for “ugly”, which means is there a non square number in front of the polynomial, and you can’t use the rest of the rules.

Simple way for factoring “ugly” polynomials:

When factoring ugly polynomials, you can either figure out exactly what numbers multiply into each of them and put them in the correct order to circle back to the original polynomial, or you can use an area model, which is the simpler way.

To use this method you have to:

  1. Take out anything in common
  2. Multiply the first and last term together, forgetting about variables
  3. Find all the ways to multiply to that number, and pick the way that adds up to the middle term
  4. Separate all the terms into 4 boxes
  5. Look horizontally to see what the 2 boxes have in common in each row
  6. Look vertically to see what those 2 boxes have in common in each column
  7. Take the numbers that were in common from each side and place them in brackets to get your factored form
  8. Do a quick check to make sure you circle back to the original question