4/14 Alg2: Remainder Theorem and Factor Theorem

The Remainder Theorem and Factor Theorem

Making our lives easier when dividing polynomials!

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can use the Remainder Theorem and Factor Theorem to evaluate polynomials.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Let's analyze some remainders!

Let's start by using synthetic division together.

Think to yourself. What is the polynomial represented by this synthetic division? (You will answer on the next slide)

Multiple Choice

What is the polynomial that we've found from this synthetic division work?

• $f\left(x\right)=x^2+5x+4$

• $f\left(x\right)=x^2+5x+4+\left(\frac{4}{x+5}\right)$
  

• $f\left(x\right)=x^3+5x^2+4x+4$
  

Multiple Choice

Evaluate P(-5).

• 4

• 25

• -17

• -29

Let's try another example together.

Let's start with the synthetic division!

Multiple Choice

What is the polynomial we've found from our synthetic division?

• $f\left(x\right)=x+6+\left(\frac{5}{x-2}\right)$

• $f\left(x\right)=x^2+6x+\left(\frac{5}{x+2}\right)$
  

• $f\left(x\right)=x^3+6x+5$
  

Multiple Choice

Evaluate f(-2).

(Is it equal to the remainder of the polynomial that we found?)

• 1

• -9

• 5

• 24

Multiple Choice

Is f(-2) equal to the remainder of the polynomial?

• Yes, that's the whole point!!!!

• No

Let's apply these theorems, shall we?

Here is a real example of this content.

Biologists and other scientists use a LOT of polynomials for their research!

Let's start by using synthetic division!

Multiple Choice

What is the remainder, according to our synthetic division work?

• 8

• 0

• 293

• -32

Multiple Choice

Put it in context. What is the estimated the population in 2023?

• 8 tortoises

• 0 tortoises

• 293 tortoises

• -32 tortoises

Debrief

Poll

Please rate your current state of understanding of the learning target.

Learning Target: I can use the Remainder Theorem and Factor Theorem to evaluate polynomials.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Great work! Move to Google Classroom and complete your exit ticket. Enjoy your Wednesday! :)