Dividing Polynomials L2.7

Polynomial Division

Lesson 2.7

This will be a graded assignment.

After lesson 2.8, you will take a quiz over both lessons.

If you want to be successful with these lessons and continue to do them instead of Edgenuity...

1) Keep organized notes in a notebook or folder.

2) Label the notes for this lesson: Polynomial Division L2.6.

3) WATCH the video included and take good notes.

4) Take the google form quiz by the end of Friday this week.

5) Give me feedback about the lesson at the end.

Let's get started. This activity should take about 45 minutes.

You already know how to do simple division like this -----> Right?

Try 2 problems like this one...

Multiple Choice

Click on the picture to make it larger.

• 5w ² − 4w + 3

• 12w ² − 9w + 6

• 12w ² − 12w + 9

• 5w ² − 12w+ 9

Multiple Choice

Divide the polynomial by the monomial.

• 15x⁹ - 8x³

• 3x⁶ - 8x³

• -5x¹²

• 3x⁶ - 40x³

FYI: Dividing polynomials can get more complicated -->

Don't write this example. I just want to prepare you for what a problem will look like. Watch the video on the next slide. TAKE NOTES along with the video. You can speed it up, slow down, pause ,as needed.

I refer to problems from the packet during the video. Open to page 25 or have notebook paper ready.

The sound quality is so-so. I'll try to make it more clear next time!

Multiple Choice

What is the divisor in this equation?

 $143\ \div\ 11\ =\ 13$  

• 143

• 11

• 13

• 0

Multiple Choice

Write the answer with the remainder as a fraction (like I taught in the video)

 $15\div2=$  

•  $7$  

•  $7.5$  

•  $7+\frac{1}{2}$  

Poll

Favorite movie genre? Pick one

• Sci-Fi/Fantasy

• Comedy

• Drama

• Action/Adventure

Multiple Choice

Let's start with an easy one. There will be no remainder when you divide. Practice showing your work using the long division method, and make sure you are able to get 2x - 7 as your answer.

(4x² - 24x + 35) / (2x - 5)

• 2x - 7

• 2x - 12

• 2x + 12

• 2x + 7

Multiple Choice

With multiple choice answers and NO remainder, it is faster to just think about which answer will multiply by the divisor to make the quotient. Do you see that the answer must be x - 10, without actually doing the long division?? Now, try one like this on the next slide.

           

 $\frac{x^2-12x+20}{x-2}$  

• x+7

• x+2

• X-10

• X-7

Multiple Choice

The area of a rectangular pool table is: x² + 14x +40.

The length is x + 4. What is the width? (Just pick out the answer that multiplies with x + 4 to make the area expression)

• x + 8

• x + 14

• x + 10

• x +4

Multiple Choice

The answer to a division problem is called the:

• Sum

• Difference

• Product

• Quotient

Get ready to try a harder one on the next slide. Refer to the examples we did together in the video.

Here's another example if you want to practice first ------>

Multiple Choice

 $\frac{2x^3+7x^2-6x-8}{x+4}$  

(Hint: no remainder!)

•  $2x^2-x-2$  

•  $2x^3-x^2-2x$  

•  $2x^2+15x+54+\frac{208}{x+4}$  

•  $2x^3+15x^2+54x+208$  

Multiple Choice

 $\frac{2x^3-5x^2-4x-25}{x-4}$  

(Hint: there is a remainder)
You will see this problem worked out on the next slide!

•  $2x^2+3x+8-\frac{57}{x-4}$  

•  $2x^2-13x-56$  

•  $2x^2+3x+8+\frac{7}{x-4}$  

•  $2x^2-3x-16-\frac{89}{x-4}$  

Notice the cancelling that should happen each time. That will help you to know what number goes next in the answer.

Poll

Candy Corn?

• Love it

• Hate it

• Indifferent

A few notes:

If there is NO remainder, that means the divisor IS A FACTOR

If there IS a remainder, that means the divisor IS NOT A FACTOR

Multiple Choice

Is 3 a factor of 20?

• Yes

• No

Multiple Choice

Decide if (x - 3) is a factor of 3x³ + 10x² - x - 12. (Hint: Do the division. If there is a remainder, choose NOT a factor. If there is no remainder, choose YES)

• Yes, it is a factor

• No, it is not a factor

Multiple Choice

Is 4x - 5 a factor of this dividend?

• Yes, because there is no remainder

• No, because there is a remainder

Multiple Choice

Which term is missing in the dividend?

(2x³ + 5x + 9) ÷ (x + 3)

• x⁴

• x³

• x²

• x

Multiple Choice

Which term is missing in the divisor?

 $(-3x^3+5x^2+9x-2)÷(x^2+3)$  

• x⁴

• x³

• x²

• x

Multiple Choice

The answer to a division problem is called the:

• Sum

• Difference

• Product

• Quotient

Multiple Choice

Find the remainder (remember to use a place holder!)

(2x³ - 5x - 7) / (x + 2)

• -9

• 11

• -13

• 1

Multiple Choice

What should you do when you miss Algebra class?

• Look at the calendar in google classroom to see what I missed and try to catch up

• Use telepathy to determine what classmates are learning and take some notes

• Sit around doing nothing and hope to catch up in class

• Have a good cry because I will never catch up

Multiple Choice

Divide.

(2x³ + 13x² + 31x + 35)/(2x + 7)

• x² + 2x + 6

• x² + 3x + 5

• x² - 3x - 8

• x² + 3x + 8

Multiple Choice

How do you know when the divisor is a FACTOR of the dividend?

• when pigs can fly

• when the remainder is 0

• when they have the same degree

• when the dividend is larger than the divisor

Multiple Choice

The area, A, of a rectangle is 120x² + 78x – 90, and the length, l, of the rectangle is 12x + 15. Which of the following gives the width, w, of the rectangle?

• 13x - 19

• 10x - 6

• 10x - 19

• 12x + 4

Poll

How well do you understand polynomial division now?

• I completely understand

• I mostly understand...need a little more practice

• I'm a little confused...need plenty of practice

• I'm very confused.

Open Ended

Do you have any specific questions or feedback for this lesson?

Next step: try the practice worksheet.