4.4: Polynomial Factoring

Goals for today! Be able to

Use the Sum & Difference of Cubes Formulas to Factor & Solve Polynomials
Apply the method of Factoring by Grouping to higher degree polynomials (4 terms)

Sum and Difference of Cubes

Factoring Sum and Difference of Cubes requires knowing these two formulas:

$LaTeX: a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)$

$LaTeX: a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$

Here is a video of a teacher doing a few examples with these formulas:

Factoring Sums and Differences of Cubes

Notice that the video explains how to factor, not necessarily how to solve. Think about how you can apply your knowledge of solving from past in this situation.

Factoring by Grouping

You have already seen factoring by grouping as a technique for factoring trinomials where a is not equal to 1. We will extend the technique to higher order polynomials with four terms.

Here is a short introduction video:

https://www.youtube.com/watch?v=biVPOqbDPK0

How does this connect to solving?

Grouping Image

Then, read the guided notes and try examples on this Khan Academy page:

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/a/factoring-by-grouping

Homework Practice: p. 184-185 #13-20 all; 23-29 all; and p. 186 #77-80

Resources:

Adding and Subtracting Polynomials: Link

Multiplying Polynomials: Link

Cubing Binomials: Link

Today's links are also contained separately in the Resource pages following.