## Reflection: Connection to Prior Knowledge Simplifying Rational Expressions, Day 2 - Section 2: Simplifying more complex expressions

I was worried (and rightly so) that my students would not simply “recall” synthetic substitution, so I decided to help them along with a "synthetic substitution reminder".

In the first part, I gave them some cues to help them recall how the procedure worked, and it turned out that only a few students had any trouble.  I was easily able to bring them back up to speed with a quick 1-on-1.

The second part moved to the more conceptual side of things: using synthetic substitution to identify factors.   This gave almost everyone trouble, so I asked a few questions to get them going.

1. “If (x – 2) is a factor of our polynomial, what does that mean for the graph?”
1. I asked this question because the graph is more familiar territory for many students.  They responded that the graph would cross the x-axis at x = 2.
2. “Why must the graph have a root at +2?  Why not at -2?”
1. I asked this question because many students want to use -2 when they do the synthetic substitution.  They correctly answered that since the factor is (x-2), the x-value that makes the factor zero is +2.
3. “Do you recall the factor theorem?”
1. Somewhat surprisingly, they did.  If f(a) = 0, then (x - a) must be a factor, and conversely.

What's the takeaway?  If synthetic substitution reveals that f(2) = 0, then (x – 2) must be a factor.  This was very helpful to many students and I saw them using this method to great advantage on the next problem set.  (Check out my whiteboard at the end of this conversation.)

Connection to Prior Knowledge: What if they don't remember?

# Simplifying Rational Expressions, Day 2

Unit 7: Rational Functions
Lesson 6 of 17

## Big Idea: Simplifying rational expressions isn't complicated until zero gets involved!

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Standards:
Subject(s):
Math, rational expressions, Algebra, Graphing (Algebra), asymptote, Function Operations and Inverses, Algebra, master teacher project, rational function, discontinuity
45 minutes

### Jacob Nazeck

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