Free Printable 1/27/25–Group Quiz: Synthetic and more

1.

(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

2.

(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

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.

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

5.

a)

2x³ + 3x + (7/x-4)

b)

2x² + 3x + 8 + (7/x-4)

c)

2x² + 3x + 8

d)

2x² - x + 10 + (6/x-4)

6.

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.

7.

a)

x + 5 + (2/2x - 4)

b)

x - 8

c)

x - 5 + (3/2x - 4)

d)

x + 5

8.

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

9.

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

10.

X intercepts are also called....

More than one answer

a)

Solutions

b)

Parabolas

c)

Roots

d)

Puppies

11.

Given a graph, how can you find the "solutions" to a quadratic?

a)

Copy off neighbor

b)

Plug into calculator

c)

Solutions are where the quadratic crosses the x axis

d)

Magic 8 Ball

12.

What are the green dots called?

a)

roots

b)

vertex

c)

solutions

d)

x intercepts

13.

What are the x- intercepts?

a)

(0,0) and (0,4)

b)

(0,0) and (4,0)

c)

y= 0

d)

x= 2

14.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

15.

Fully Factor the Following
8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

16.

64x³ + 1

a)

(4x - 3)(16x² + 12x + 9)

b)

(3x - 1)(9x² + 3x + 1)

c)

(2x - 1)(4x² + 2x + 1)

d)

(4x + 1)(16x² - 4x + 1)

17.

$xy\left(x-1\right)$

a)

$x^2y^2-xy$

b)

$x^2y-1$

c)

$x^2y-xy$

d)

$xy^2-xy$

18.

$\left(x-1\right)\left(2x+1\right)$

a)

$2x^2-1$

b)

$2x^2-x+1$

c)

$2x^2-x-1$

d)

$2x^2+x-1$

19.

$\left(2x-y\right)\left(x-y\right)$

a)

$2x^2-3xy+y^2$

b)

$2x-3xy+y$

c)

$2x^2-3xy-y^2$

d)

$2x+3xy-y$

20.

$4y\left(2x^2-3x+4\right)$

a)

$8x^2y^2-12xy+16y$

b)

$8xy^2+12xy+16y$

c)

$8x^2y-12xy+16y$

d)

$4xy+16y$

21.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

22.

(3x − 6)(7x + 7)

a)

21x² − 63x + 42

b)

21x² − 21x − 42

c)

21x² − 42

d)

21x² + 63x + 42

23.

What is the first question you ask yourself when factoring a polynomial?

a)

How many terms does it have?

b)

Is there a GCF?

c)

What strategy should I use?

d)

Why do I have to learn this?!?!?!

24.

Factor completely:

5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

25.

Factor completely:

81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

26.

Factor completely:

3x² + 18x +15

Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Cannot be factored

27.

Factor completely:

x⁴-9x²

Hint: Factor GCF first.

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

28.

Factor completely:

3x² - 7x + 2

a)

(x - 1) (3x + 2)

b)

(x - 2) (3x -1)

c)

(x - 1) (3x - 2)

d)

(x + 2) (3x + 1)

29.

Factor completely:

8x³-27

a)

(2x+3)(4x²-6x+9)

b)

(2x-3)(4x²+6x+9)

c)

(2x-3)(4x²+6x-9)

d)

(2x-3)(2x²+6x+9)

30.

Factor completely:

4h² - 12h + 9

a)

(2h - 3)²

b)

4(h + 9)(h + 1)

c)

(2h - 3)(2h + 3)

d)

(h - 9)(4h - 1)

31.

Factor completely:

25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

32.

Factor completely:

64x³+125

a)

(4x+5)(16x²-20x+25)

b)

(4x-5)(16x²+20x+25)

c)

(4x-5)(4x²+20x-25)

d)

(4x-5)(4x²+20x+25)

33.

(4x²+ x) - (x²+ 2x)

a)

3x² - x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

34.

Simplify the expression.
-4(9 + 3x) - 4(x - 2)

a)

-16x-28

b)

-16x-44

c)

20x - 12

d)

30x - 9

35.

Simplify each expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

36.

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

37.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

38.

$Subtract:\ \ \left(13a^2-6a^5-2a\right)-\left(-10a^2-11a^5+9a\right)$

a)

$-17a^5-23a^2-11a$

b)

$15a^5-23a^2+11a$

c)

$27a^7-11a$

d)

$5a^5+23a^2-11a$

39.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

40.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

41.

Multiply:
(2-5i)(2+5i)

a)

29

b)

4 - 25i

c)

25 - 10i

d)

-21

42.

(2i)(3i)

a)

5i

b)

-5

c)

6i²

d)

-6

43.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

44.

Which expression is equivalent to (-6 + i)²?

a)

36 - 12i

b)

35 - 12i

c)

36i²

d)

35i

45.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

46.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

47.

What does i² = ?

a)

-1

b)

$\sqrt{-1}$

c)

1

d)

$-\sqrt{1}$

48.

Calculate (multiply):
(4 + 3i)(4 − 3i)

a)

16 − 9i²

b)

25

c)

7

d)

8 − 6i

49.

Simplify $\sqrt{-45}$

a)

$3i\sqrt{5}$

b)

$-3i\sqrt{5}$

c)

$-i\sqrt{45}$

d)

45i

50.

If the standard form of a complex number is written as $a+bi$ , which is the imaginary part?

a)

$a$

b)

$bi$

c)

$a+bi$

d)

$x^2$

1/27/25–Group Quiz: Synthetic and more

Total questions: 50

Worksheet time: 13hrs 30mins

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