Free Printable Polynomial algebra 26-1-22

1.

An AREA formula is given: $A=lw$

Which shape can you find the area of using this formula?

a)

Triangle

b)

Circle

c)

Rectangle

d)

Parallelogram

2.

Find the area of the given rectangle.

a)

$42x^3+28x^2$

b)

$42x^2+28x^{ }$

c)

$42x^3+4x^2$

d)

$13x^3+11x^2$

3.

Find the area of the given rectangle.

a)

$40x^5-25x^4+15x^3$

b)

$40x^5-25x^4+3x^3$

c)

$13x^5-10x^4+8x^3$

d)

$40x^2-25x^{ }+15$

4.

When multiplying a polynomial by a monomial, what property is used?

a)

Addition Property

b)

Distributive Property

c)

Division Property

d)

Subtraction Property

5.

Multiply by distributing.

a)

$3x^4-18x^3+15x^2$

b)

$3x^2-18x+15$

c)

$3x^4-9x^3+8x^2$

d)

$3x^4-18x^2+15x^2$

6.

Multiply by distributing.

a)

$30x^4-10x^3$

b)

$11x^4-7x^3$

c)

$30x^{ }-10$

d)

$30x^4-2x^3$

7.

You can find the PERIMETER of a polygon by multiplying all side lengths together.

a)

True

b)

False

8.

The following image is a square. Find the PERIMETER AND AREA of the polygon.

a)

PERIMETER: $16x^3$ AREA: $16x^6$

b)

PERIMETER: $16x^6$ AREA: $16x^3$

c)

PERIMETER: $8x^3$ AREA: $8x^6$

d)

PERIMETER: $8x^6$ AREA: $8x^3$

9.

The following image is a triangle. Find the PERIMETER and AREA of the polygon.

a)

PERIMETER: $22x$ AREA: $35x^2$

b)

PERIMETER: $35x$ AREA: $22x^2$

c)

PERIMETER: $360x$ AREA: $70x^2$

d)

PERIMETER: $22x$ AREA: $70x^2$

10.

When multiplying like bases, you __________ exponents.

a)

ADD

b)

SUBTRACT

c)

MULTIPLY

d)

DIVIDE

11.

Find the area of the given rectangle.

a)

$18x^2-48x+6$

b)

$18x^3-48x+6x$

c)

$18x^3-48x^2+6x$

d)

$9x^3-14x^2+7x$

12.

Find the area of the given rectangle.

a)

$7x^5-3x^3+2$

b)

$7x^7-3x^5+2x^2$

c)

$7x^{14}-3x^6+2x^2$

d)

$7x^7-3x^6+2x^2$

13.

If x²+kx+6 = (x+2)(x+3) for all k, find the value of k.

a)

-1

b)

1

c)

3

d)

5

14.

One of the factors of (1 + 3y)² + (9y² – 1) is

a)

1-3y

b)

3-y

c)

3y+1

d)

y-3

15.

Which of the following operations are polynomials always closed under? Select ALL the APPLY

a)

Addition

b)

Division

c)

Multiplication

d)

Subtraction

16.

Which of the following Operations are Polynomials NOT CLOSED under?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

17.

When a polynomial is divided by a polynomial, we say that quotients are

NOT __________________ under division because the quotients of a polynomial and a polynomial IS NOT a polynomial.

a)

NOT Closed

b)

NOT Open

18.

Use the distributive property to simplify the following express. SHOW YOUR WORK. "NWNC"

2(3x - 4)

a)

6x - 8

b)

6x + 8

c)

5x - 6

d)

5x + 6

19.

What does the word difference mean?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

20.

What is the difference for the following polynomials? SHOW YOUR WORK "NWNC"

(3x² - 4x + 5) - (4x² + 5x - 3)

a)

-x² - 9x + 8

b)

x² - 9x + 8

c)

-x - 9x + 8

d)

x - 9x + 8

21.

What does the word sum mean?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

22.

What is the sum of the following polynomials? SHOW YOUR WORK "NWNC"

(3x² - 4x + 5) + (4x² + 5x - 3)

a)

7x² + x + 2

b)

7x² + 9x + 8

c)

7x⁴ + x + 2

d)

-7x² - x + 2

23.

Mr. Early has a rectangular garden in his back yard with an area of 3x² square meters. He decided to make it larger and the new area will be (3x² + 4x + 5) square meters. What is the difference between the new garden and the original garden? Show your work. "NWNC"

a)

4x + 5

b)

9x² + 4x + 5

c)

-4x + 5

d)

x² + 4x + 5

24.

What does the word Product mean?

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

25.

Find the product of

(3x – 2) and (3x² - 4x + 5) ?

Use the area model. "NWNC"

a)

9x³ - 18x² + 23x - 10

b)

-9x³ + 18x² + 23x - 10

c)

9x² - 18x + 13

d)

9x⁴- 18x³ + 23x² - 10x

26.

How do you find perimeter of a shape/figure?

a)

Add of the Sides togeather

b)

Length x Width

c)

Multiply all the sides

d)

Divide?

27.

a)

10m³ + 2m² - m - 5

b)

10m⁹ + 2m⁶ - m² - 5

c)

10m³ - 2m² +9m - 5

d)

10m³ + 2m² -9m - 5

28.

What is the product of 5x and (-3x² - 4x + 5) ?

Hint: Remember ADD the exponents when multiplying.

a)

-15x³ - 20x² + 25x

b)

15x³ + 20x² + 25x

c)

-15x² - 20x - 25

d)

15x² + 20x - 25

29.

Find the product for the following binomials. Use the are model. "NWNC"

(2x - 6)(-3x + 2)

a)

-6x² - 14x - 12

b)

6x² + 14x - 12

c)

-6x² - 22x - 12

d)

-6x² + 22x - 12

30.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

31.

What are the x-intercepts of
f(x)=(x - 10)(x + 10)

a)

10

b)

(10 , 0) and (-10 , 0)

c)

(0, -10) and (0, 10)

d)

0

32.

a)

(-2.55, 0), (2.55, 0)

b)

(-3, 0), (-2, 0), (2, 0), (3, 0)

c)

(0, 36)

d)

(0, -3), (0, -2), (0, 2), (0, 3)

33.

Describe the end behavior of
f(x) = 2x² + 6x⁵ + 10x

a)

Left side: Rises
Right side: Rises

b)

Left side: Falls
Right side: Rises

c)

Left side:Rises
Right side: Falls

d)

Left side: Falls
Right side: Falls

34.

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

35.

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

36.

Describe the type of polynomial shown.

a)

Even degree, negative leading coefficient

b)

Even Function

c)

Odd degree, negative leading coefficient

d)

Even degree, positive leading coefficient

37.

What is the leading coefficient?

a)

Positive

b)

Negative

38.

What is the factored form of a function if it has zeros of 2, 3 and -1?

a)

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

b)

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

c)

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

d)

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

39.

Classify by degree of polynomial:
3x² – 8x + 1

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

40.

Is the leading coefficient positive or negative

a)

positive

b)

negative

41.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

Left side: Rises
Right side: Rises

b)

Left Side: Rises
Right side: Falls

c)

Left side: Falls
Right side: Rises

d)

Left side: Falls
Right side: Falls

42.

If a zero of a polynomial function has multiplicity 3 that means:

a)

The x intercept is at (4, 0)

b)

The graph will "bounce back" at that zero

c)

The graph will "pass through" at that zero

d)

Zeros cannot have multiplicity of 4

43.

Which of the following allows you to describe the end behavior of a polynomial?

a)

the degree and the constant

b)

the leading coefficient and the constant

c)

degree and the variable

d)

the degree and the leading coefficent

44.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

45.

In the above graph, which root has a multiplicity of 2?

a)

-1

b)

-3

c)

-120

d)

4

46.

f(x)=(x+4)(x-3)(x-2)

List the zeros for this function.

a)

x=-4, x=3, x=-2

b)

x=-4, x=3, x=2

c)

x=-4, x=3, x=-2

d)

x=4, x=3, x=2

47.

Select all the even degree functions.

a)

A

b)

B

c)

C

d)

D

48.

Which functions have a negative leading coefficient?

a)

A

b)

B

c)

C

d)

D

49.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

Left side: Rises
Right side: Rises

b)

Left Side: Rises
Right side: Falls

c)

Left side: Falls
Right side: Rises

d)

Left side: Falls
Right side: Falls

50.

For $f\left(x\right)\ =\ 7x^3-x^2-6x+9$ , what is $f\left(3\right)$ ?

a)

-171

b)

153

c)

171

d)

189

51.

For $f\left(x\right)\ =\ 7x^3-x^2-6x+9$ , what is $f\left(-3\right)$ ?

a)

-171

b)

153

c)

171

d)

189

52.

For $f\left(x\right)\ =\ 7x^3-x^2-6x+9$ , what is $f\left(3\right)$ ?

a)

-171

b)

153

c)

171

d)

189

53.

For $f\left(x\right)\ =\ 7x^3-x^2-6x+9$ , what is $f\left(-3\right)$ ?

a)

-171

b)

153

c)

171

d)

189

54.

For $f\left(x\right)\ =\ 7x^3-x^2-6x+9$ , what is the degree?

a)

2

b)

3

c)

0

d)

1

55.

What is $f(x)=8-7x^3-3x^5+2x+8x^2$ in standard form?

a)

$f(x)=8+2x+8x^2-7x^3-3x^5$

b)

$f(x)=-3x^5-7x^3+8x^2+2x+8$

c)

$f(x)=3x^5-7x^3+8x^2+2x-8$

d)

$f(x)=3x^5+7x^3-8x^2-2x-8$

56.

For $f(x)=8-7x^3-3x^5+2x+8x^2$ , as $x\rightarrow-\infty$ , what happens?

a)

$f\left(x\right)\rightarrow\infty$

b)

$f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow\infty$

d)

$f\left(x\right)\$ explodes

57.

For $f(x)=8-7x^3-3x^5+2x+8x^2$ , as $x\rightarrow\infty$ , what happens?

a)

$f\left(x\right)\rightarrow\infty$

b)

$f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty$

d)

$f\left(x\right)\$ explodes

58.

If $f\left(x\right)$ has a positive, odd degree, what shape will it have?

a)

A sideways S-ish shape going in this direction \

b)

A U-ish shape opening up

c)

A U-ish shape opening down

d)

A sideways S-ish shape going in this direction /

59.

If $f\left(x\right)$ has a negative, even degree, what shape will it have?

a)

A sideways S-ish shape going in this direction /

b)

A U-ish shape opening up

c)

A U-ish shape opening down

d)

A sideways S-ish shape going in this direciton \

60.

Can I pass this math class?

a)

I won't pass, but I'm trying

b)

I will pass if I try hard

c)

I will pass without trying

d)

I'm not trying, so I won't pass

61.

Find the common factors of the following:-

 6 xyz, 24 xy2 and 12 x2y

a)

6xy

b)

x2 y2

c)

6x²

62.

Find the common factors of the following:-

3x² y³, 10x³ y² and 6x² y² z

a)

x²y²

b)

2xyz

c)

xyz

63.

Factorise the following expression:-

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

a)

8x-14x-30

b)

8x²+14x-15

c)

8x²-14x+15

64.

Factorise the following expression:-

(y-8)(3y-4)

a)

3y³+28y-32

b)

3y+14y²+16

c)

3y²-28y+32

65.

Factorise the following expression:-

(2pq+3q²)(3pq-2q²)

a)

6pq²-5pq³-6p²

b)

6p²q²+5pq³-6q⁴

c)

6p²q²-5pq³-6q⁴

66.

Factorise the following trinomials:-

x² + 7x +10

a)

(x + 5)(x -2)

b)

(x + 5)(x + 2)

c)

2x(x-5)

67.

Factorize the following trinomials:-

x² + 5x + 6

a)

(x + 2)(x + 3)

b)

(x - 2)(x -3)

c)

x(x+2)(x-3)

68.

State whether the following expression is difference of a square or not:-

x²-100

a)

yes

b)

no

69.

State whether the following term is difference of a square or not:-

x-36

a)

yes

b)

no

70.

Factorize the following polynomials:-

x² + 3x - 10

a)

(x - 2) (x + 5)

b)

(x - 3) (x - 6)

c)

x(x+5)(x+3)

71.

Factor the following polynomial:-

x² + 2x - 24

a)

(x - 2) (x + 5)

b)

(x - 4) (x + 6)

c)

(3 x + 2) (x + 1)

72.

Factorize the following expression:-

20a2 – 45b2

a)

5(a+3b)(a-3b)

b)

(a + 8)(a – 8)

c)

5(2a + 3b)(2a – 3b)

73.

Factorise the following expression:-

x2 – 2xy + y2 – z2

a)

8(2xy + 1)(2xy – 1)

b)

(x – y – z)(x – y + z)

c)

2x(y-z)(y+z)

74.

Find out the common factors:-

14x,21y²

4 lines

75.

Factorize by regrouping terms:-

z-6+6xy-xyz

a)

x(6+xy)

b)

(z-6)(1-xy)

c)

x(z-6)(1-y)

76.

Factorize $x^2+3xy+2x+6y$ completely.

a)

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

b)

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

c)

$\left(x-3y\right)\left(x-2\right)$

d)

$\left(x-3\right)\left(x-2y\right)$

e)

Not Factorable (Prime Polynomial)

77.

Factorize $1-121x^2$ completely.

a)

$\left(1-11x\right)\left(1-11x\right)$

b)

$\left(1-11x\right)^2$

c)

$\left(1-11x\right)\left(1+11x\right)$

d)

$\left(1+11x\right)\left(1+11x\right)$

78.

Factorize $pn^2+3np-28p$ completely.

a)

$p\left(n+4\right)\left(n-7\right)$

b)

$p\left(n-4\right)\left(n+7\right)$

c)

$p\left(n+4\right)\left(n+7\right)$

d)

$p\left(n-4\right)\left(n-7\right)$

79.

Factorize $a^2\ +13a\ +\ 36$ completely.

a)

$\left(a-4\right)\left(a-9\right)$

b)

$\left(a-4\right)\left(a+9\right)$

c)

$\left(a+4\right)\left(a-9\right)$

d)

$\left(a+4\right)\left(a+9\right)$

80.

Factorize $q^2-7q-18$ completely.

a)

$\left(q+2\right)\left(q-9\right)$

b)

$\left(q-2\right)\left(q+9\right)$

c)

$\left(q+3\right)\left(q-6\right)$

d)

$\left(q-3\right)\left(q+6\right)$

81.

Factorize $9f^2+18f-16$ completely.

a)

$\left(3f+2\right)\left(3f-8\right)$

b)

$\left(3f-2\right)\left(3f-8\right)$

c)

Not Factorable (Prime Polynomial)

d)

$\left(3f-2\right)\left(3f+8\right)$

82.

Factorize $3x^2+12x+12$ completely.

a)

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

b)

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

c)

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

d)

Not Factorable (Prime Polynomial)

83.

Factorize $ax-5a+4x-20$ completely.

a)

$\left(x-4\right)\left(a+5\right)$

b)

$\left(x+4\right)\left(a-5\right)$

c)

$\left(x-5\right)\left(a+4\right)$

d)

$\left(x+5\right)\left(a-4\right)$

84.

Which of the following is an example of a difference between two squares?

a)

$9x^2-27y^2$

b)

$4x^2-100y^2$

c)

$8x^2-25y^2$

d)

$81x^2+16y^2$

85.

Which of the following is an example of a perfect square trinomial?

a)

$16x^2-40xy+25y^2$

b)

$16x^2-20xy+25y^2$

c)

$4x^2-10xy+25y^2$

d)

$4x^2-14xy+5y^2$

86.

FOR POLYNOMIALS, IF QUESTION ASKED TO FACTORIZE COMPLETELY, WHAT WE NEED TO DO?

a)

SQUARING BOTH SIDES

b)

LONG DIVISION

c)

CRAMER'S RULE

d)

USE CALCULATOR

87.

ANSWER FOR THIS QUESTION NEED TO RECHECK

a)

TRUE

b)

FALSE

88.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

89.

Classify:
2n³

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

90.

What are like terms?
Terms that have....

a)

the same variables

b)

the same exponents

c)

the same coefficients

d)

the same variables and exponents

91.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

92.

Simplify by combining like terms:
4x² - 3x + 11 -2x

a)

4x² - 5x + 11

b)

11x + 11

c)

16x² - 5x + 11

d)

10x²

93.

The number in front of the variable is called the....

a)

exponent

b)

base

c)

coefficient

d)

fronter

94.

Which pair is an example of like terms?

a)

2a and 2b

b)

x and x²

c)

3k and 3k³

d)

y² and 2y²

95.

What is the the DEGREE:

4x³ - 5x² + 2x - 1

a)

1

b)

2

c)

3

d)

4

96.

What is the coefficient of this term?

9x³

a)

None

b)

9

c)

3

d)

x

97.

Simplify the Expression:

3x + 6 - 2x +7

a)

14

b)

14x

c)

x + 13

d)

x - 13

98.

Simplify this polynomial:

3x²- x + 2 - 5x²+ 8x - 5

a)

8x²+ 9x + 7

b)

-2x²+ 7x - 3

c)

2x²+ 7x - 3

d)

5x²- 3

99.

Simplify this polynomial:

n - 10 + 9n - 3

a)

-3

b)

9n - 3

c)

n

d)

10n - 13

100.

Classify by number of terms:

5x² – 6x + 3

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

101.

What is the constant of this polynomial?

2x³- 8x²+ 3x - 7

a)

2

b)

-8

c)

3

d)

-7

102.

What is the degree of this polynomial?

2x⁴- 3x⁵+ x

a)

-3

b)

2

c)

4

d)

5

103.

How many terms are in this polynomial?

2x³- 8x²+ 3x - 7

a)

7

b)

1

c)

4

d)

2

104.

Factor: x² + 13x + 30

a)

(x + 3)(x + 10)

b)

(x + 5)(x + 6)

c)

(x + 2)(x + 15)

d)

(x + 1)(x + 30)

105.

Factor: x² - 16x + 24

a)

(x + 2)(x - 14)

b)

(x - 2)(x - 14)

c)

(x + 14)(x - 2)

d)

(x - 4)(x - 6)

106.

Factor: x² - 2x - 24

a)

(x + 6)(x - 4)

b)

(x + 4)(x - 6)

c)

(x - 4)(x - 6))

d)

(x - 3)(x + 8)

107.

Factor: x² + 13x - 48

a)

(x + 3)(x - 16)

b)

(x + 16)(x - 3)

c)

(x + 4)(x - 12)

d)

(x + 12)(x - 4)

108.

Expand and simplify the following quadratic expression...

(x + 3)(x + 2)

a)

x² + 5x + 6

b)

x² + 5x + 5

c)

x² + 6x + 6

d)

x² + 6x + 5

109.

Expand and simplify the following quadratic expression...

(x + 4)(x + 6)

a)

x² + 10x + 24

b)

x² + 10x + 10

c)

x² + 24x + 10

d)

x² + 24x + 24

110.

Expand and simplify the following quadratic expression...

(x - 6)(x - 4)

a)

x² - 10x + 24

b)

x² - 10x - 24

c)

x² + 10x - 24

d)

x² + 10x + 24

111.

Factorise the following quadratic expression...

x² + 14x + 24

a)

(x + 12)(x + 2)

b)

(x + 8)(x + 3)

c)

(x + 4)(x + 6)

d)

(x + 24)(x + 1)

112.

Factorise the following quadratic expression...

x² + 12x + 32

a)

(x + 16)(x + 2)

b)

(x + 8)(x + 4)

c)

(x + 6)(x + 6)

d)

(x + 32)(x + 1)

113.

Factorise the following quadratic expression...

x² + 12x + 32

a)

(x + 16)(x + 2)

b)

(x + 8)(x + 4)

c)

(x + 6)(x + 6)

d)

(x + 32)(x + 1)

114.

Factorise the following quadratic expression...

x² + 13x + 40

a)

(x + 8)(x + 5)

b)

(x + 10)(x + 4)

c)

(x + 20)(x + 2)

d)

(x + 40)(x + 1)

Polynomial algebra 26-1-22

Total questions: 114

Worksheet time: 2hrs 56mins

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