This week in class we did some review on factoring from grade 10, and then we had a lesson on factoring polynomial expressions. For example, when we reviewed factoring from grade 10, we would be given something like 15x^3 – 5x^2 and told to factor it. When factoring we were shown to use steps following the acronym CDPEU, this stands for Common, Difference of squares, Pattern, Easy, Ugly. So for this question, you start with Common, and you look for something that you can divide out of all the terms. In this questions you can take out 5x^2 out of all the terms, so you would then have 5x^2(3x – 1). Then you would look to see if it is a difference of squares, and it is not because not all of the terms can be squared. Then you would look to see if there is a pattern, which would be the easy pattern x^2  x  #, or the ugly pattern, which would be ax^2  x   #, for this question, it doesn’t fit either pattern, so you cannot factor any further. So your final answer would be 5x^2(3x – 1).

The picture bellow is of the question I just went over:

When doing more complicated questions you would be given something like 3y(y+2) – 9(y+2). With this question the first thing in noticed is the two terms have the same thing in brackets (common difference). So you would then have (y+2)(3y – 9), the next thing you do is take out the common difference between 3y and -9 which is 3, so you would then have 3(y+2)(y – 3). From here you cannot factor any further so you leave it the way it is.

The picture bellow is of the question I just went over: