This week we did factoring polynomials.

When factoring polynomials, there is list of things you should go over so you know when to stop factoring:

  1. Is there anything common in the polynomial?
  2. Is it a difference of squares? (only works for binomials)
  3. Is there a pattern? (x^2 , x , #)
  4. If there is a pattern is it “easy” or “ugly”? (easy has no coefficient in front of the x^2 , the ugly one does)

Here’s an example of one where you apply the first step to:
16x^3 - 4x^2

As you can see there is a common factor of 4x^2

So the factored version would be 4x^2(4x - 1)

Here’s an example for difference of squares:

x^2 - 49

You can tell this is a difference of squares since the perfect square 7 goes into 49, the x is squared, and there is a subtraction sign.

So from here you would just factor and use the conjugate:

(x – 7) (x +7)

Here is an example of what to do when you see the pattern:

x^2 + 8x + 15

First, you should look at the factors of 15:

1 x 15

3 x 5

Then you just have to choose which one adds up to 8, so 5 and 3.

Then you will end up with a binomial starting with x, and ending in the two numbers. It will be addition since the x and the 15 are both positive:

(x + 3) (x + 5)

If you were to simplify this you would end up with the expression you started with.