This week in math 10 we learned how to factor ugly polynomials. And a quick way to do it.
a phrase that will help you make sure you are doing all the steps correctly and in order is CDPEU a way to remember these letters in order is: can divers pee easily underwater. The C in the phrase stands for common which means you need to figure out if the numbers have anything of common. The D stands for difference of squares, the way you know if it is a difference of squares question is if is it a binomial is there a subtract symbol and are they all perfect squares. The P is pattern for this you look to see if there is a pattern to solve the question easier. The E is easy so just look to see if it is an easy question. Then lastly U which stands for ugly this is when there is a non square number in front of the polynomial if it is this one you can’t use the rest of the rules.
For factoring an ugly polynomial the first step is to try and find if it has anything in common with all the terms and divide. Then you rewrite the question but in the simplified form and you want to put that number you divided the terms by in front of the bracket. Then you make a square divided into four parts, the first term in your polynomial is going to go in the top left box and the last term is going to go in the bottom right box, then you multiply those coefficient together after finding the answer you want to find the factors of that number and pick the factors that add to the middle term if the answer you got from multiplying the coefficients is a negative you just make the bigger factor of the two a nagative and add them. Then you put those factors into the remaining boxes and you have to add an x to the end of both the numbers. Then you go across the rows and down the collombs finding the common factor in the numbers writing the answer alonf the vertical and horzontal part on the outer sides of the square then you put those numbers into the brackets putting the verticals factors into a bracket and the horizontal factors into a bracket and you put the number you divided the first terms with at the front of the first bracket and then you have your factored ugly polynomial.