Free Printable 2.5-2.8 Review

1.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

2.

(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

3.

(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

4.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

5.

(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

6.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

7.

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.

8.

What does i²= ?

a)

1

b)

-1

c)

√-1

d)

√1

9.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

10.

Simplify:

(10 + 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

11.

Find the sum.

(5 - 2i) + (-7 + 8i)

a)

-2 + 6i

b)

12 + 6i

c)

-35 - 16i²

d)

-35 - 16i

12.

Multiply:

(2 - 5i)(2 + 5i)

a)

29

b)

4 - 25i

c)

25 - 10i

d)

-21

13.

(2i)(3i)

a)

5i

b)

-5

c)

6i²

d)

-6

14.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

15.

Simplify √-45

a)

3i√5

b)

-3i√5

c)

-i√45

d)

45i

16.

Simplify √-1

a)

1

b)

-i

c)

-1

d)

i

17.

Simplify √-4

a)

2i

b)

-2i

c)

2

d)

4i

18.

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

a)

36 - 12i

b)

35 - 12i

c)

36i²

d)

35i

19.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

20.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

21.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

22.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

23.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

24.

Which of the following roots match the above polynomial:

a)

-3,-1,4

b)

-3,2i,-2i

25.

If x-2 is a factor of x^2+5x+7, then that means.....

a)

f(0) = 2

b)

f(0) = -2

c)

f(2) = 0

d)

f(-2) = 0

26.

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

a)

f(x) = (x+2)(x-1)(x-4)

b)

f(x) =x³ - 3x² - 6x + 8

c)

f(x) = x³+ 8

d)

f(x) = x³ - 3x² + 8

27.

If a+bi is a root of a polynomial, then _______ is also a root.

a)

i²

b)

a-bi

c)

a+bi

d)

-i²

28.

Find a polynomial function of degree 3 with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

29.

Write the polynomial with the given zeros

a)

A

b)

B

c)

C

d)

D

30.

Identify the zeros:

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

31.

a)

Positive Odd

b)

Positive Even

c)

Negative Odd

d)

Negative Even

32.

Over the interval (−1, 2), the graph of the polynomial shown could be described as

a)

decreasing

b)

increasing

c)

quadratic

d)

complex

33.

What are the zeros of the polynomial function?

y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

34.

Even Multiplicities have which of the following effects on the x-axis?

a)

touches and bounces back

b)

wiggle

c)

crosses the x-axis

35.

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

36.

Use the quadratic formula to solve
2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

37.

What is the name of the imaginary line that cuts a parabola in half and goes through the vertex?

a)

the middle

b)

axis of symmetry

c)

minimum

d)

standard form

38.

Solve using the Quadratic Formula:
x² + 4x + 3 = 0

a)

x = 1 and x = 3

b)

x = 6 and x = -2

c)

x = -1 and x = -3

d)

x = 2 and x = 3

39.

Solve using the quadratic formula:
4x²+ 4x + 1 = 0

a)

x = -½

b)

x = -2

c)

x = 0

d)

x = 1

40.

Match the complex expressions on the left with the correct simplified value on the right.

a)

$\left(12+6i\right)-\left(7-2i\right)$

1.

$5+8i$

b)

$\left(2+5i\right)\left(1+4i\right)$

2.

$-18+13i$

c)

$\left(2-2i\right)\left(6-3i\right)$

3.

$6-18i$

d)

$\left(8+2i\right)+\left(3-4i\right)$

4.

$11-2i$

41.

Match each expression to its factored form

a)

$6x^2+x-1$

1.

(3x-1)(2x+1)

b)

$x^2+6x+9$

2.

(x+3)²

c)

$3x^2+12x+12$

3.

3(x+2)²

d)

$2x^2-18$

4.

2(x+3)(x-3)

42.

Match each polynomial to its factored form:

a)

$x^2+5x+4$

1.

(x+4)(x+1)

b)

$x^2-5x+4$

2.

(x-4)(x-1)

c)

$x^2+3x-4$

3.

(x+4)(x-1)

d)

$x^2-3x-4$

4.

(x-4)(x+1)

43.

Which of the following is equivalent to w³ + 3w

(a)

Choose from the below words

w (w2+3)

3w (w2+1)

There is no GCF

2.5-2.8 Review

Total questions: 43

Worksheet time: 4hrs 58mins

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