Free Printable Polynomial Unit Test

1.

Rewrite the following polynomial in standard form:

-5x^2+7-3x+2x^{\text{4}}

a)

$2x^4-5x^2-3x+7$

b)

$7+5x^2+2x^4-3x$

c)

$-3x+2x^4-5x^2+7$

d)

$-3x+2x^{\text{4}}+7-5x^2$

2.

What is the leading coefficient of the following polynomial?

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

a)

$-1$

b)

$-3$

c)

$8$

d)

$-9$

3.

What is the degree of the following polynomial?

-7x-5x^2+10+2x^4

a)

$1$

b)

$7$

c)

$-5$

d)

$4$

4.

Classify the polynomial by number of terms.

$x^3+5x^2+14$

a)

Polynomial

b)

Trinomial

c)

Binomial

d)

Monomial

5.

Polynomial written in descending order, from largest to smallest degree.

a)

Standard Form

b)

Leading Coefficient

c)

Degree

d)

Constant Term

6.

The number in front of the first term of a polynomial.

a)

Standard Form

b)

Leading Coefficient

c)

Degree

d)

Constant Term

7.

Classify the polynomial by number of terms.

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

a)

Polynomial

b)

Trinomial

c)

Binomial

d)

Monomial

8.

Multiply.
-3x²(7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

9.

(4x³-5x²+3x)+(-2x³-x²+6x)

a)

2x³-6x²-9x

b)

2x³+6x²+9x

c)

-2x³-6x²+9x

d)

2x³-6x²+9x

10.

Factor completely

45xy + 15x³y + 10y

a)

5y (9xy + 3x²+ 2y)

b)

5xy (9 + 3x²+ 2)

c)

5x (9y + 3xy + 2)

d)

5y (9x + 3x³ + 2)

11.

Add or Subtract to Simplify:
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

a)

4b⁴ - 2b³ + 7

b)

5b⁴ - 2b³ + 4

c)

b⁴ - 2b³ + 7

d)

5b⁴ - 2b³ + 7

12.

(4x + 7)(3x + 5)

a)

12x + 41 + 35

b)

12x² + 20x + 35

c)

12x² + 41x + 35

d)

12x + 20 + 35

13.

(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

14.

Give the correct name for
2x³+5x

a)

Linear Binomial

b)

Cubic Binomial

c)

Quadratic Trinomial

d)

Linear Trinomial

15.

(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

16.

Divide 8x² -4x + 12 by 2x

a)

4x+2

b)

4x-2+6/1x

c)

4x-2

d)

4x-2+12/2x

17.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

18.

Simplify (multiply)
(3x²)(3x⁴y³)

a)

A
9x⁶y³

b)

B
3x⁶y³

c)

C
6x⁸y³

d)

D
6x⁸y⁶

19.

Multiply.
(2b+3)x(3b²+2b+1)

a)

A
6b³+ 6b²+ 6b + 3

b)

B
6b³+ 13b²+ 8b + 3

c)

C
5b³+ 8b²+ 3b + 4

d)

D
5b³+ 6b²+ 3b + 4

20.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

21.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

22.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

23.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

24.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

25.

Find all zeros for the polynomial function $f\left(x\right)=x^3-3x^2+12x-10$

a)

$1,\ 1\pm3i$

b)

$1,\ -1\pm3i$

c)

$-1,-1\pm3i$

d)

$-1,\ -5,\ 2$

26.

$h\left(t\right)=2t^2-7t$ find $h\left(-1\right)$

a)

$h\left(-1\right)=-5$

b)

$h\left(-1\right)=9$

c)

$h\left(-1\right)=-9$

d)

$h\left(-1\right)=5$

27.

If f(x) = -4x - 5 and

g(x) = 3 - x,

what is g(-4) + f(1)?

a)

7

b)

-2

c)

-9

d)

-10

28.

What does multiplicity of a zero mean?

a)

Look at the number of terms

b)

How many times the zero repeats

c)

Find the sum of all the coefficients

d)

Ratio your x and y

29.

Find all roots/zeros/x-intercepts/solutions.

a)

$x=0,\ 1\ \pm2i\sqrt{6}$

b)

$x=0,\ 1\ \pm i\sqrt{22}$

c)

$x=0,\ 1\ \pm5i$

d)

$x=0,\ 1\ \pm\sqrt{26}$

30.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

31.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

32.

What are the decreasing interval(s)?

a)

(- ∞, 0) & (2, ∞ )

b)

(-1, 0) & (2,-4)

c)

(0,2)

d)

(0, -4) & (0, 2)

33.

Is the leading coefficient positive or negative

a)

positive

b)

negative

34.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

35.

What is the name of a polynomial with two terms?

a)

monomial

b)

binomial

c)

trinomial

d)

quadratic

36.

What is the name of a polynomial with only one term?

a)

monomial

b)

binomial

c)

trinomial

d)

linear

37.

What is the name of a polynomial with three terms?

a)

monomial

b)

binomial

c)

trinomial

d)

cubic

38.

What is the name of a polynomial with four or more terms?

a)

monomial

b)

binomial

c)

cuatromial

d)

polynomial

39.

What is the name of a polynomial with four or more terms?

a)

monomial

b)

binomial

c)

cuatromial

d)

polynomial

40.

What is the name of the degree of a monomial that does not have a variable?
( ex. 511 )

a)

constant

b)

linear

c)

quadratic

d)

cubic

41.

What is the name of the degree of a polynomial that has a variable with invisible exponents?
( ex. n or n¹ )

a)

constant

b)

linear

c)

quadratic

d)

cubic

42.

What is the name of the degree of a polynomial that has an exponent of 2?
( ex. n squared or n² )

a)

constant

b)

linear

c)

quadratic

d)

cubic

43.

What is the name of the degree of a polynomial that has an exponent of 3?
( ex. t cubed or t ³ )

a)

constant

b)

linear

c)

quadratic

d)

cubic

44.

What is the name of a 4^th degree polynomial ?
( ex. x⁴ or m²n²)

a)

quartic

b)

fourtic

c)

quadratic

d)

cubic

45.

What is the name of a 5^th degree polynomial ?
( ex. x⁵ or mn⁴ or r²s³)

a)

constant

b)

linear

c)

quadratic

d)

quintic

46.

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

47.

When you combine like terms, what do you do with the exponents?

a)

Add them

b)

Multiply them

c)

Nothing

48.

When you multiply polynomials, what do you do with the exponents?

a)

Add them

b)

Multiply them

c)

Nothing

49.

When you multiply polynomials, what do you do with the coefficients?

a)

Add them

b)

Multiply them

c)

Nothing

50.

Factor the polynomial completely:
36x³ - 60x² + 45x - 75

a)

12x²(3x-5) - 15(3x-5)

b)

(12x²+15)(3x-5)

c)

12x²(3x-5) - 45x+75

d)

(36x³ - 60x²) + (4x - 75)

51.

What is f(x) - g(x), if

f\left(x\right)=5x^2+9x-8

and

g\left(x\right)=8x+3

.

a)

$5x^2+x-8$

b)

$5x^2+x-5$

c)

$5x^2+x-11$

d)

$5x^2+17x-5$

52.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

53.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

54.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

55.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

56.

Which option below is the same as (f∘g)(x) (How can you rewrite this)

a)

f(x)*g(x)

b)

f(g(x))

c)

g(f(x))

d)

(f*g)(x)

57.

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

58.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

59.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

60.

f(x)= x+3

g(x)= x-2

Find (g(x) / f(x))

Be careful!!

a)

(x + 3)/(x - 2)

b)

(x - 2)/(x + 3)

c)

-2/3

d)

3/2

Polynomial Unit Test

Total questions: 60

Worksheet time: 2hrs 10mins

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