Free Printable Math 4 Unit 3 Review

1.

Classify

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

2.

Classify by the DEGREE:
3x - 2

a)

1

b)

2

c)

3

d)

4

3.

Polynomial or not?
5x⁴ - 7x

a)

polynomial

b)

not a polynomial

4.

Polynomial or not?

a)

polynomial

b)

not a polynomial

5.

Rewrite the polynomial in standard form:-5 + 4m

a)

-5 + 4m

b)

4m - 5

c)

-4m + 5

d)

4m² - 5

6.

What is the leading coefficient of the following polynomial?
5x²-3x+6

a)

2

b)

-3

c)

5

d)

6

7.

Classify the polynomial by its number of terms.
4x² - 2

a)

A
monomial

b)

B
binomial

c)

C
trinomial

d)

D
polynomial

8.

How many terms are in the following polynomial?
_3xy_{- 2y + 8x - 7z -16}

a)

A
1

b)

B
2

c)

C
4

d)

D
5

9.

Add:
(3x² - 3x + 2) + (x² - 2x + 1)

a)

A
4x³-2x²+2

b)

B
4x² - 5x + 3

c)

C
-2x³+2x+2

d)

D
4x³-2x²-2

10.

What is the standard form of the polynomial,
7x - 125 - 6x⁴ + 14x²

a)

125 + 7x - 14x² +6x⁴

b)

6x⁴ -14x² - 7x +125

c)

125 + 14x² + 7x - 6x⁴

d)

-6x⁴+ 14x² + 7x - 125

11.

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

12.

(2n + 2)(6n + 1)

a)

12n + 2

b)

12n² + 2

c)

12n² + 12n + 2

d)

12n² + 14n + 2

13.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

14.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

15.

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)

16.

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?!?!?!

17.

Factor completely:

81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

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

18.

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

19.

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)

20.

Solve for the values of x:
(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

21.

Solve for the values of x:
(x - 3)(x + 6) = 0

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

22.

Which algebraic expression is shown above?

a)

$6x+3$

b)

$-3x+6$

c)

$3x+6$

d)

$9x$

23.

Based on the algebra tiles, what is the original polynomial?

a)

3x² - 3x + 2

b)

x² - 3x + 2

c)

x² - 3x - 2

24.

Write the expanded (general) form of the product (x+3)(x+6).

a)

$x^2+18x+9$

b)

$x^2+9x+18$

c)

$x^2+18x+18$

d)

$x^2+3x+18$

25.

Multiply

(2x +1) (x - 3)

a)

$2x^3-4x+3$

b)

$2x+5x-3$

c)

$2x^2-5x-3$

d)

$3x-2$

26.

$\left(x\ +\ 3\right)^2$

a)

$x^2\ +\ 3x\ +\ 15$

b)

$x^2\ +\ 9$

c)

$x^2\ -6x\ +\ 9$

d)

$x^2\ +\ 6x\ +9$

27.

What term belongs in the ? box?

(a)

28.

Find the degree of the polynomial.

a)

27

b)

12

c)

13

d)

28

29.

What is the degree of the monomial?

2x²y³z

a)

2

b)

3

c)

5

d)

6

30.

Factor completely
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

31.

Solve by Factoring: x² + 15x + 44 = 0

a)

x=-8, 2

b)

x=-7, 5

c)

x=-11, -4

d)

x=-11

32.

Factor the greatest monomial :
2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

33.

Factor:

a)

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

b)

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

c)

$x-5$

d)

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

34.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

35.

Factor this difference of cubes:
x³ - 343

a)

(x + 7)(x² - 7x + 49)

b)

(x - 7)(x - 7)(x - 7)

c)

(x - 7)(x² + 7x + 49)

d)

(x + 7)(x + 7)(x + 7)

36.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

37.

Is this a polynomial or not?

a)

Yes

b)

No

38.

Is this a polynomial or not?

a)

Yes

b)

No

39.

Which of the following is NOT a polynomial?

a)

𝑥² − 4𝑥 + 4

b)

4 + 3𝑥 ⁻²

c)

2𝑥𝑦³ − 𝑥 ²𝑦 ² + 5𝑥y

d)

11 − 7𝑥 ²

40.

Which of the following is TRUE about polynomials?

a)

The variables are raised to a negative or fractional exponent.

b)

Each term is a constant, a variable, or a product of a constant and variable in which the variable has a whole number (non-negative) exponent.

41.

The term 𝑥𝑦 ⁻² is a polynomial.

a)

True

b)

False

42.

$2x^5-x^{-2}$

a)

Polynomial

b)

Not a Polynomial

43.

Simplify

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

44.

Solve by Factoring:
x² + 15x + 64 = 20

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

45.

Solve (x²-9) = 0

a)

x = 9

b)

x = 9, -9

c)

x = 3, -3

d)

x = 3

46.

Solve the equation by factoring. Hint: This question will be on the exam!!
$x^3-49x=0$

a)

$x=0,7,-7$

b)

$x=7,-7$

c)

$x=0,7$

d)

$x=0,49$

47.

Which of the following are examples of like terms?

a)

2 and 2x

b)

y³and x³

c)

y and x

d)

-3x and 3x

48.

What is the constant in the polynomial x²-2x+5?

a)

1

b)

2

c)

5

d)

0

49.

How many terms are in a binomial??!

a)

4

b)

None

c)

3

d)

2

50.

-5x⁶(3x² - 12x + 30)

a)

-15x⁸+ 60x⁷- 150x⁶

b)

15x⁸- 60x⁷- 150x⁶

c)

8x⁶- 17x + 35

d)

-8x⁶+ 17x - 35x²

51.

The length of a rectangle is four times the width. Given that the area is 100 square inches, find the length of the rectangle.

a)

4

b)

5

c)

20

d)

50

52.

The length of a rectangle is 3 km more than the width. If its area is 40 km², find the dimensions of the rectangle.

Hint: Area = length ∙ width

a)

width = 5 km

length = 8 km

b)

width = 7 km

length = 10 km

c)

width = 2 km

length = 20 km

53.

The length of a rectangle is 3 km less than five times the width. If its area is 36 km², find the dimensions of the rectangle.

Hint: Area = length ∙ width

a)

width = 6 km

length = 6 km

b)

width = 3 km

length = 12 km

c)

width = 2 km

length = 14 km

54.

Factor: 20 – x – x²

a)

(x + 5)(x + 4)

b)

(x + 5)(x – 4)

c)

-1(x + 5)(x – 4)

55.

Solve the following Equation: This WILL be on the exam!!! x³ + 14x² + 48x = 0

a)

x = 0, x = -6, x = -8

b)

x = 6, x = 8

c)

x = 14, x = 6

d)

x = 1

56.

What is the first step into solving the following polynomial equation? x² – 10x = 24

a)

Add 24 to both sides of the equation.

b)

Divide both sides by x.

c)

Factor the left side of the equation.

d)

Move all terms to one side of the equation, so one side can equal zero. Done by subtracting 24 to both sides.

57.

Solve the following polynomial equation: x² – 10x = 24

a)

x = 6, x = -4

b)

x = 12, x = -2

c)

x = 0, x = 24

d)

x = 10, x = 14

58.

What would be the repeated factor when factoring the following trinomial through grouping? 3x² – 13x + 4

a)

x - 4

b)

x + 4

c)

3x - 1

d)

x - 1

59.

Why isn't the expression 17x^-2y³ considered a monomial?

a)

The expression contains a variable with a negative exponent.

b)

The coefficients in the expression are not whole numbers.

c)

The expression includes a variable with a fractional exponent.

d)

The expression has too many variables to be a monomial.

60.

In the given polynomial function of f(x) = 2x² – x, how do you solve for f(3)?

a)

Leave the x's alone and not solve.

b)

Substitute in 3 for the x's and evaluate/simplify to gain 15

61.

What is (2x + 5)²

a)

4x² + 10x + 20

b)

2x² + 10x + 5

c)

2x² + 25

d)

4x² + 20x + 25

62.

Why is the degree of the polynomial of 2x³y² – 5x³ + 7x⁴yz³degree of 8?

a)

The exponents of the highest degree in the term 7x⁴yz³are added. That is 4 + 1 + 3. Including variables without exponents, which is degree 1.

b)

Only add the visible exponents.

63.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

64.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

65.

What does the F in FOIL stand for?

a)

Fire

b)

First

c)

Friends

d)

Fabulous

66.

What does the O in FOIL stand for?

a)

Only

b)

Orange

c)

Outlandish

d)

Outer

67.

What does the I in FOIL stand for?

a)

Inner

b)

Imaginary

c)

Inception

d)

Ice, baby ice.

68.

What does the L in FOIL stand for?

a)

Least

b)

Lark

c)

Last

d)

Lower

69.

What does FOIL stand for?

a)

Failing Only in Latin

b)

Farming Only in Lakewood

c)

First Outside Inside Last

d)

Fresh Only in Lakes

70.

Which represents the First product using the FOIL method?

a)

$\left(5\right)\left(7\right)=35$

b)

$\left(5\right)\left(2z\right)=10z$

c)

$\left(3z\right)\left(2z\right)=6z^2$

d)

$\left(3z\right)\left(7\right)=21z$

71.

Which represents the Outer product using the FOIL method?

a)

$\left(5\right)\left(7\right)=35$

b)

$\left(5\right)\left(2z\right)=10z$

c)

$\left(3z\right)\left(2z\right)=6z^2$

d)

$\left(3z\right)\left(7\right)=21z$

72.

Which represents the Inner product using the FOIL method?

a)

$\left(5\right)\left(7\right)=35$

b)

$\left(5\right)\left(2z\right)=10z$

c)

$\left(3z\right)\left(2z\right)=6z^2$

d)

$\left(3z\right)\left(7\right)=21z$

73.

Which represents the Last product using the FOIL method?

a)

$\left(5\right)\left(7\right)=35$

b)

$\left(5\right)\left(2z\right)=10z$

c)

$\left(3z\right)\left(2z\right)=6z^2$

d)

$\left(3z\right)\left(7\right)=21z$

74.

What method is being used in the image?

a)

FIND

b)

FIOL

c)

FOIL

d)

FIRE

75.

Is 4x² + 9y²factorable? On Exam!!!

a)

No!!!!! 4x² + 9y² is not factorable. There is no such thing as sum of 2 squares!

b)

Yes, 4x² + 9y² can be factored as (2x + 3y)(2x - 3y). Difference of 2 squares.

76.

How would you factor 2x⁴ – 162? Hint: think GCF and Difference of 2 Squares! You might see this again!

a)

2(x - 3)(x + 3)(x² + 9)

b)

2(x - 9)(x + 9)

Math 4 Unit 3 Review

Total questions: 76

Worksheet time: 4hrs 1mins

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