Sec. 3.4 (Synthetic Division) - Alg 2 Diff

​Sec. 3.4:

Synthetic

Division

​Materials Needed:

​1) Chapter 3 Note Packet (begin on p. 6)

2) Pencil and Calculator​

​Before beginning the lesson, please write down one thing you are thankful for in the margin of your notes. Thank you!

​Please watch the 9-minute video on the next slide and complete the notes in your note packet as you watch.

​Please complete the following problems. Use another sheet of paper to show your work.

Multiple Choice

Divide using synthetic division:

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

• 3x³ - 5x² - 2x + 8
• 3x² + x - 6
• 3x² - 5x - 2 + 8/x+1
• 3x³ + x² - 6x

Multiple Choice

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0
• 2
• 4
• 6

Multiple Choice

What is the proper way to write the answer for the following problem?

• 2x³-x²-25x+12

• 2x⁴-x³-25x²-12x+0

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x-0

Multiple Choice

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

• Cam wrote the remainder incorrectly.

• Cam did not use a zero place holder for the x³ term.

• Cam added instead of subtracting the rows.

• Cam should have used -2 as his division since the factor was x-2.

Multiple Choice

Was this problem done correctly?

• Yes

• No

Multiple Choice

What is the next step in synthetic division?

• Add the -48 to the 54

• Multiply the 54 and 6

• Divide the 54 by 6

• Bring down the -58

Multiple Choice

What is the next step in synthetic division?

• Multiply the 9 and 6

• Add the 9 and 6

• Bring down the -48

Multiple Choice

What is the remainder when x⁴ - 5 is divided by x + 3?

• 76

• 81

• 7

Multiple Choice

Divide using synthetic division 
(2x³ + 4x² - 5) by (x + 3).

• 2x² + 2x - 4  R(-12)
• 2x² - 2x + 6  R(-23)
• 2x² - 2x + 8  R(-20)
• 2x² - 4x + 1  R0

​Please watch the 4-minute video on the next slide and complete the notes in your note packet as you watch.

​If you would like to see another example when the coefficient of the divisor is not a 1, see the video on the next slide. Otherwise, skip that slide.

​Please complete the following problems. Use another sheet of paper to show your work.

Multiple Choice

Divide using synthetic division:

$$\left(2x^2+6x-20\right)\div\left(2x-4\right)$$  

• $$x+5+\frac{2}{2x-4}$$  

• $$x-8$$  

• $$x-5+\frac{3}{2x-4}$$  

• $$x+5$$   

Multiple Choice

Divide using synthetic division

(the optional video clip will help with this problem)

  $$(4x^4-3x^3-4x^2-x+3)\ ÷\ (4x-3)$$  

• $$x^3+x^2+x-1$$

• $$x^3-x-1$$

• $$x^3-2x-1$$

• $$x^3-x^2+x-3$$

Multiple Choice

Use synthetic division to find the remainder when

3x² + 5x + 10 is divided by 3x ─ 1 .

• 3

• 6

• 12

​Please watch the 7-minute video on the next slide and complete the notes in your note packet as you watch.

Multiple Choice

If f(x) = 5x² ─ 7x ─10, find the value of f (5) using synthetic division.

• 150

• 80

• 70

Multiple Choice

Given P(x) = x³ + x² – x ─ 9, use direct substitution to find the value of P(4)?

• 14

• -53

• 67

Multiple Choice

if f(x) = 3x² - 9x - 20, find the value of f(5) using synthetic division. Confirm your answer by using direct substitution as well.

• 0
• 10
• 15
• -7

​Thank you for your participation today! Please make note of any questions you have from this lesson. Have a great day!