Free Printable 2/2/24 Group Synthetic and Factoring Quiz

1.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

2.

(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

3.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

4.

Let f(x) = 4x² -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

5.

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

6.

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.

7.

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

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

8.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

9.

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

10.

Which term is missing in this problem?
2x³ + 5x² + 9 ÷
x + 3

a)

x⁴

b)

x³

c)

x²

d)

x

11.

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

12.

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

13.

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

a)

0

b)

1

c)

2

d)

3

14.

(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

15.

(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

16.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

17.

(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

18.

(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

19.

(2x³ + 7x² - 6x - 8) ÷ (x + 4)

a)

2x² - x - 2

b)

2x³ - x² - 2x

c)

2x² + 15x + 54 + 208/x+4

d)

2x³ + 15x² + 54x + 208

20.

Let f(x) = 3x^2 - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

21.

Let f(x) = 4x^2 -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

22.

x³-3x²-10x+24 ÷ x+3

a)

x²-7x+5

b)

x-8

c)

x²-6x+8

d)

x+9

23.

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

24.

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

a)

0

b)

1

c)

2

d)

3

25.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

26.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

27.

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

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

28.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

29.

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

a)

True

b)

False

c)

Only for the dividend

d)

Only for the divisor

30.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

31.

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

32.

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

33.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

34.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

35.

$\left(2x^5+5x^4-14x^3+17x^2-7x-3\right)\div\left(x-1\right)$ Is x-1 a factor of the polynomial?

a)

Yas

b)

No

36.

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

a)

The remainder is zero

b)

They are all factors

c)

We can't tell

d)

The remainder is a constant

37.

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.

38.

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

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

39.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

40.

Complete the square for

x² + 12x + ____

(find the missing number in the blank)

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

41.

Complete the square for

x² - 14x + ____

(find the missing value that goes in the blank)

a)

- 196

b)

49

c)

- 49

d)

28

42.

Complete the square for

x² + 6x + ____

(find the missing value that goes in the blank)

a)

9

b)

12

c)

36

d)

- 9

43.

Is this a perfect square trinomial? (Will it factor into 2 common factors?)

x² + 18x + 9

a)

Yes

b)

No

44.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

45.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

46.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

47.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

48.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

49.

Factor the perfect square trinomial:
x² + 16x + 64

a)

(x+8)²

b)

(x-8)²

c)

(x-4)²

d)

(x+4)²

50.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

51.

Factor the following:

$x^2-10x+25$

a)

$\left(x-5\right)\left(x-5\right)$

b)

$\left(x+5\right)\left(x-5\right)$

c)

$\left(x-5\right)\left(x+5\right)$

52.

Factor the following:

$x^2-6x+9$

a)

$\left(x-3\right)\left(x+3\right)$

b)

$\left(x-3\right)\left(x-3\right)$

c)

$\left(x+3\right)\left(x+3\right)$

53.

Factor the following:

$x^2+14x+49$

a)

$\left(x-7\right)\left(x+7\right)$

b)

$\left(x-7\right)\left(x-7\right)$

c)

$\left(x+7\right)\left(x+7\right)$

54.

Put the steps to Completing the Square in the correct order

a)

Move constants to one side

b)

add $\left(\frac{b}{2}\right)^2$ to both sides

c)

Factor the trinomial

d)

Take the square root of both sides.

e)

Solve both cases.

1)

2)

3)

4)

5)

55.

What is the first step to completing the square for this equation?

0 = x² + 10x + 21

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add x² and 10x together

d)

Subtract 21 on both sides

56.

Complete the square but do not solve.

$x^2+10x\ -11=0$

a)

$\left(x+5\right)^2=36$

b)

$\left(x+5\right)^2=25$

c)

$\left(x+10\right)^2=100$

d)

$\left(x+10\right)^2=111$

57.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

58.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

59.

Solve for x by taking the Square Root:

(x+6)²= 49

a)

x = 7 and 12

b)

x = ±7

c)

x = 1 and -13

d)

x = 43 and -55

2/2/24 Group Synthetic and Factoring Quiz

Total questions: 59

Worksheet time: 15hrs 45mins

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