Factoring Polynomials

This week in math we learned how to factor polynomials.

Factoring polynomials were first introduced in grade 10 and now we are expanding our knowledge.  To understand how to factor a polynomial we were introduced to an acronym CDPEU, these letters stand for:

COMMON: is there anything common throughout the whole polynomial that divides evenly?

DIFFERENCE OF SQUARES: does anything have a relationship with a perfect square, which allows you to use conjugates?

PATTERN: is it a trinomial? Do the variable as well as finding two numbers that are factors of the product and add or subtract to the middle number?

EASY: are the coefficients easy to deal with?

UGLY: is the first coefficient greater than one? (You will have to use the box method, or guess and check)

When factoring a polynomial if you go through each of these letters and their meaning and then ask yourself if they relate to the polynomial you are trying to solve it makes solving polynomials a lot easier.

So, if the polynomial I had to factor was:

Then I would ask myself if there is anything common?  In this case, no.  Then I would ask myself if it is a difference of squares?  Meaning you are easily able to square rot each number, in this case, no as well.  Next, I need to ask my self if there is a pattern.  My answer to that is yes, there is a pattern.

Now, I know X will be in each component since the polynomial includes an X squared.

Next, I have to find factor 14 and out of those factors find two numbers that add to 9.   In this case, those two numbers are 2 and 7.

Finally, I have to pay attention to the negatives and positives.  In this case, all are positive so I don’t have to worry.

In the end, it should look like this:

But, if 9 was negative this means that both factors, 2 and 7 must be negative.  But, if 14 was also negative, 7 must be negative since there would be more negatives then positives and 7 is greater than 2.

Now you know how to solve polynomials through the method using the pattern.