## Reflection: Rigor Factoring Completely - Section 4: Closure

Today's ticket out (factor_completely1_close) showed that most students had a decent understanding of factoring completely.  Namely, they were able to say that an expression is factored completely when the individual factors cannot be factored any further (they are prime factors).

I had a little extra time at the end of this lesson so I wanted to show students an example of an expression that could be factored more than twice.  The expression x^8 - 1 is interesting because it can be factored multiple times (note: x^(any even power greater than 2) - 1) can be factored multiple times.  Letting students go through factoring this expression solidified the idea of looking at the factors each time to determine which can be factored further.  Solution is shown below and can be generalized for higher even powers than 8.

x^8 - 1

(x^4-1)(x^4+1)

(x^2-1)(x^2+1)(x^4+1)

(x-1)(x+1)(x^2+1)(x^4+1)

Rigor: An Addition to the Lesson

# Factoring Completely

Unit 4: Polynomial Expressions
Lesson 17 of 18

## Big Idea: This lesson uses a graphic organizer to help students factor and multiply polynomial expressions.

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40 minutes

### James Bialasik

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