Free Printable Synthetic Division

1.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

2.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

3.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

4.

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

a)

0

b)

2

c)

4

d)

6

5.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

6.

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

7.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

8.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

9.

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

a)

Cam wrote the remainder incorrectly.

b)

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

c)

Cam added instead of subtracting the rows.

d)

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

10.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

11.

What would be the coefficients we use to solve:

$\frac{\left(5x^7+3x^6-9x^4+4x^3+2x-37\right)}{x+1}$

a)

$5,\ \ 3,-9,\ \ 4,\ \ 2,-37$

b)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 0,\ \ 2,-37$

c)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2,-37$

d)

$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2$

12.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

13.

What is the next step in synthetic division?

a)

Bring the 6 down

b)

Multiply the 9 and 6

c)

Bring the 9 down

d)

Add the 9 and 6

14.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 9 and 6

c)

Bring down the -48

15.

What is the next step in synthetic division?

a)

Add the -48 to the 54

b)

Multiply the 54 and 6

c)

Divide the 54 by 6

d)

Bring down the -58

16.

What is the next step in synthetic division?

a)

Multiply the 9 and 6

b)

Add the 6 and -58

c)

Bring down the -58

d)

Divide the -58 by 6

17.

It's time to write the answer. What goes in the yellow area?

a)

$n-9$

b)

9

c)

-9

d)

$6n^2-48n-58$

18.

Find the quotient:

(3x³ + 5x - 1) ÷ (x + 1)

a)

3x³ - 3x² + 8x - 9

b)

3x² - 3x + 8 - 9/x+1

c)

3x² + 3x + 8 + 7/x+1

d)

3x³ + 3x² + 8x + 7

19.

Find the quotient:

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

20.

Find the quotient:

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

Synthetic Division

Total questions: 20

Worksheet time: 2hrs 38mins

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