Free Printable Polinomi

1.

$f\left(x\right)=x^3-3x^2-25x+75$ Find the zeros of the polynomial given one factor. $x=5$

a)

X= -3,5,-5

b)

x=-3,5,-5

c)

x=-3,4,5

d)

x= 3, 5, -5

2.

$f\left(x\right)=x^3-5x^2-2x+24;\ \ \ -2$ Find all rational zeros, one zero has been given.

a)

-2,1,0

b)

-2,-3,-4

c)

4,3,-2

d)

0,0,0

3.

Which best describes the multiplicity of a root?

a)

It is the number of times the corresponding factor is repeated

b)

It is the highest degree of the polynomial

c)

It is the number of times x is multiplied by itself

d)

It is the number of x-intercepts on a graph

4.

The degree of a polynomial determines...

a)

the maximum number of x-intercepts

b)

the number of turning points

c)

if the end behavior is up or down

d)

the y-intercept

5.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

6.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

7.

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

8.

What are the

zeros of the polynomial

y = 5(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, 5, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 5

9.

a)

A

b)

B

c)

C

d)

D

10.

What is the degree?

a)

Odd

b)

Even

11.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

12.

$f\left(x\right)=x^3-3x^2-25x+75$ Find the zeros of the polynomial given one factor. $x=5$

a)

X= -3,5,-5

b)

x=-3,5,-5

c)

x=-3,4,5

d)

x= 3, 5, -5

13.

$f\left(x\right)=x^3-5x^2-2x+24;\ \ \ -2$ Find all rational zeros, one zero has been given.

a)

-2,1,0

b)

-2,-3,-4

c)

4,3,-2

d)

0,0,0

14.

$Given\ f\left(x\right)=3x^3-4x^2-28x-16$ .

Which number below is zero of f(x)?

a)

8

b)

-2

c)

6

d)

1

15.

$If\ f\left(x\right)=2x^3-9x^2-123x-220$ , which value below is a root?

a)

18

b)

4

c)

11

d)

-7

16.

Find all zeros for the polynomial
$P\left(x\right)=x^3-3x^2-5x+15$

a)

$3,\sqrt[]{5}$

b)

$3,\sqrt[]{5},-\sqrt[]{5}$

c)

$-3,\sqrt[]{5},-\sqrt[]{5}$

d)

$-3,5i,-5i$

17.

FInd all zeros for the polynomial
$f\left(x\right)=x^4+8x^2-9$

a)

$-1,\frac{1}{3},\pm3i$

b)

$-1,\frac{1}{2},\pm3i$

c)

$-1,1,\pm i\ \sqrt[]{11}$

d)

$-1,1,\pm3i$

18.

Which is the graph of $\left(x+5\right)^2\left(x+3\right)$ ?

a)

b)

c)

d)

19.

A 5th degree polynomial function with roots of $\sqrt{3},\ -\sqrt{3},-\frac{7}{2},\ 2i,\ -2i$ , will have how many x-intercepts?

a)

2

b)

3

c)

4

d)

5

20.

If $\left(x+1\right)$ and $\left(x+3\right)$ are two factors of $x^3-x^2-17x-15$ , find the other one.

a)

$x-5$

b)

$x+5$

c)

$x+1$

d)

$x-12$

21.

Which description(s) best fit the graph of F(x)? Select all that apply. (Could you draw a graph given a description?)

a)

odd function

b)

Zeros at 1/2, 2, and 4

c)

positive lead coefficient

d)

A possible multiplicity at 2

22.

Write a polynomial function of least degree with integral coefficients and have zeros 2, 1, -1.

a)

x³ - 2x² - x + 2

b)

x³ + 2x² - x + 2

c)

x³ - 2x² - x - 2

d)

x³ - 2x² + x + 2

23.

Write a polynomial function of least degree with integral coefficients and have zeros 3, - 1, 1, 2

a)

x⁴ - 5x³ + 5x² + 5x - 6

b)

x⁴ + 5x³ + 5x² + 5x - 6

c)

x⁴ - 5x³ - 5x² + 5x - 6

d)

x⁴ - 5x³ + 5x² + 5x + 6

24.

Write a polynomial function of least degree with integral coefficients and have zeros 4, -4, i, -i

a)

x⁴ - 15x²+ 16

b)

x³ - 15x² - 16

c)

x⁴ - 15x² - 16

d)

x⁴ -17x² - 16

25.

The function shown has:

a)

Degree two with negative leading coefficient.

b)

Degree three with negative leading coefficient.

c)

Degree four with negative leading coefficient.

d)

Degree four with positive leading coefficient.

26.

Which of the following could be a possible equation for the function shown?

a)

f(x) =-2x³ + x² - 5x + 1

b)

f(x) = 2x³ - 4x² + x + 1

c)

f(x) = 3x² + 5x + 1

d)

f(x) = -2x³ +3x - 1

27.

Write the equation of the graph in factored form, given the y-intercept is (0, -72). Hint- you will need to solve for a

(a)

28.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

29.

If you know the degree of this polynomial is 4, describe the type of roots it has.

a)

Two real roots

Two imaginary roots

b)

Four real roots

c)

Four imaginary roots

d)

Two real roots

One imaginary root

30.

Which polynomial has 6 roots?

a)

$5x^4+2$

b)

$6x^5-4x-5$

c)

$5x^5+12x^3+7x^2+15$

d)

$7x^6+3x^3+12$

31.

Identify the zeros

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

32.

Which equation is the polynomial in factored form?

a)

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

b)

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

c)

f(x) = (x-4)²(x-1)(x+2)²

d)

f(x) = (x+4)²(x+1)(x-2)²

33.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

34.

Find all complex roots of the polynomial. $x^3+2x^2+4x+8=0$

a)

$\left\{2,\ 2i,\ -2i\right\}$

b)

$\left\{-2,\ 2i,\ -2i\right\}$

c)

$\left\{-2,\ 2,\ -2i,\ 2i\right\}$

d)

$\left\{2,\ 2i\right\}$

35.

SELECT ALL that are real factors of a polynomial with zeros $x=-3\ and\ -2i$

a)

$\left(x+3\right)$

b)

$\left(x-3\right)$

c)

$\left(x^2+4\right)$

d)

$\left(x^2-4\right)$

36.

Which shows the polynomial factored into complex linear factors? $x^4+4x^2-32=0$

a)

$\left(x-2\right)\left(x+2\right)\left(x-i\sqrt{8}\right)\left(x+i\sqrt{8}\right)$

b)

$\left(x-2i\right)\left(x+2i\right)\left(x-\sqrt{8}\right)\left(x+\sqrt{8}\right)$

c)

$\left(x-2\right)\left(x+2\right)\left(x-\sqrt{8}\right)\left(x+\sqrt{8}\right)$

d)

$\left(x-2i\right)\left(x+2i\right)\left(x-i\sqrt{8}\right)\left(x+i\sqrt{8}\right)$

37.

Write a polynomial function of least degree in factored form that has the follow roots.
$-3,\ \sqrt{5}$

a)

$f\left(x\right)=\left(x+3\right)\left(x^2+5\right)$

b)

$f\left(x\right)=\left(x+3\right)\left(x-\sqrt{5}\right)$

c)

$f\left(x\right)=\left(x+3\right)\left(x-5\right)$

d)

$f\left(x\right)=\left(x-3\right)\left(x-\sqrt{5}\right)$

38.

Write a polynomial function of least degree in factored form that has the follow roots.
$3,\ -3i$

a)

$f\left(x\right)=\left(x-3\right)\left(x+3i\right)$

b)

$f\left(x\right)=\left(x-3\right)\left(x^2+9\right)$

c)

$f\left(x\right)=\left(x+3\right)\left(x+9\right)$

d)

$f\left(x\right)=\left(x-3\right)\left(x-9\right)$

39.

Find all complex roots.
$f\left(x\right)=x^3-2x^2+x-2$

a)

$\left\{2,\ 1\right\}$

b)

$\left\{-2,\ 2,\ -1,\ 1\right\}$

c)

$\left\{2,\ 1\ ,\ 1\right\}$

d)

$\left\{2,\ 1,\ -1\right\}$

40.

Write the polynomial in standard form given the following zeros. $x=-5,\ 2$

a)

f\left(x\right)=\left(x+5\right)\left(x+2\right)

b)

$f\left(x\right)=x^2+3x-10$

c)

$f\left(x\right)=x^4-29x^2+100$

d)

$f\left(x\right)=\left(x^2-25\right)\left(x^2-4\right)$

41.

Write the polynomial in standard form given the following zeros. $x=-1,\ \pm i$

a)

$f\left(x\right)=\left(x+1\right)\left(x^2-1\right)$

b)

$f\left(x\right)=x^2-2x+1$

c)

$f\left(x\right)=x^3+x^2+x+1$

d)

$f\left(x\right)=x^3-x^2-x+1$

42.

Which of the following polynomials is factored entirely into linear factors?

a)

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

b)

$f\left(x\right)=x\left(2x+3\right)\left(x^2+5\right)$

c)

$f\left(x\right)=x^3\left(3x-5\right)\left(x^2-2\right)$

d)

$f\left(x\right)=x\left(x-3\right)\left(x+3\right)$

43.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

44.

$f\left(x\right)=x^3+3x^2-x-3$
What are the roots of the function (select all that apply)

a)

-3

b)

-1

c)

1

d)

2

45.

$f\left(x\right)=x^3-4x^2+x+6$
What are the roots of the function (select all that apply)

a)

-1

b)

1

c)

2

d)

3

46.

$f\left(x\right)=x^3+2x^2-25x-50$
What are the roots of the function (select all that apply)

a)

-5

b)

-2

c)

2

d)

5

47.

$f\left(x\right)=x^3-6x^2+11x-6$
What are the roots of the function (select all that apply)

a)

1

b)

2

c)

3

d)

4

48.

$f\left(x\right)=x^3-2x^2-3x$
What are the roots of the function (select all that apply)

a)

-1

b)

0

c)

2

d)

3

49.

$f\left(x\right)=x^3-3x^2-6x+8$
What are the roots of the function (select all that apply)

a)

-2

b)

1

c)

2

d)

4

50.

$f\left(x\right)=x^3+2x^2-15x$
What are the roots of the function (select all that apply)

a)

-5

b)

0

c)

1

d)

3

51.

State the zeros of the polynomial function $f\left(x\right)=x\left(x+3\right)^2\left(x-2\right)$

a)

0, 2, -3

b)

0, 2, -3 multiplicity 2

c)

2, -3 mulitiplicity 2

d)

0, -2, 3 multiplicity 2

52.

How many zeros does the polynomial function $f\left(x\right)=3x^4+4x^{2\ }+8$ have?

a)

2

b)

3

c)

4

d)

6

53.

Which of the following is the correct equation for the function graphed?

a)

$f\left(x\right)=\left(x-1\right)^{2\ }\left(x+2\right)^{2\ }$

b)

$f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^{2\ }$

c)

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

d)

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

54.

Which is a possible equation in factored form of the function in the graph?

a)

$y=\left(x+2\right)\left(x-1\right)^2$

b)

$y=\left(x-2\right)\left(x+4\right)\left(x+1\right)^2$

c)

$y=-\left(x+2\right)\left(x-1\right)^2$

d)

$y=-\left(x+1\right)^2\left(x-2\right)$

55.

What is the degree of the polynomial? $f\left(x\right)=-2x\left(x+3\right)^2\left(x-7\right)\left(x+5\right)^3$

a)

6

b)

7

c)

5

d)

3

56.

How does a factor with multiplicity of 2 affect the graph of a polynomial function?

a)

Touch and Turn

b)

Straight Through

c)

"Snake" Through

d)

Touch, Flatten, and Turn

57.

What are the roots for $\left(x-3\right)^2\left(x+1\right)$ ?

a)

1,-3

b)

-1,3

c)

-3 only

d)

3 only

58.

Which equation MOST LIKELY matches the graph?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

59.

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

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

a)

-1

b)

-3

c)

-120

d)

4

60.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

61.

What is the factored form of the function graphed?

a)

y = -(x+6)(x-5)(x-8)

b)

y = -(x-6)(x+5)(x+8)

c)

y = -(x-5)(x-8)

d)

y = -(x+6)(x-5)

62.

Which solution has a multiplicity of 2?

a)

-1

b)

1

c)

3

d)

none of them do

63.

Perhatikan bentuk aljabar berikut !
(i) $x^{3\ }-\ 3x^2\cos\pi\ -\ 2x\ +\ 4$
(ii) $x^{3\ }-\ 3x^{2\ }+\ \cos3x\ +\ 3$
(iii) $x^{3\ }-\ 3x^{2\ }-\ \frac{x}{2}\ +\ 4$
(iv) $x^{3\ }-\ 3x^{2\ }-\ \frac{4}{x}\ +\ 4$

a)

( i ) dan ( ii )

b)

( i ) dan ( iii )

c)

( i ) dan ( iv)

d)

( ii ) dan ( iii )

e)

( iii) dan ( iv )

64.

Perhatikan bentuk aljabar berikut.
(i) $x^3-3x^2-2x+5$
(ii) $x^3-3x^2+\sin3x+3$
(iii) $x^3-3x^2-\frac{x}{2}+4$
(iv) $x^4-3x^2-\frac{4}{x}+3$
Bentuk aljabar yang merupakan polinomial adalah ....

a)

(i) dan (ii)

b)

(i) dan (iii)

c)

(i) dan (iv)

d)

(ii) dan (iii)

e)

(iii) dan (iv)

65.

Dari polinomial $x^6+4x^5-5x^2+x-2\$ diperoleh pernayataan-pernyataan berikut.
(i) Banyak suku polinomial ada 5.
(ii) Suku konstanta polinomial adalah 2.
(iii) Derajat polinomial adalah 6.
Pernyataan yang benar adalah ....

a)

(i) saja

b)

(ii) saja

c)

(iii) saja

d)

(i) dan (ii)

e)

(i) dan (iii)

66.

Terdapat bentuk aljabar dibawah ini !
(i) $7x^{4\ }+\ 3x^3-10x^2\ -\ 9$
(ii) $x^{90}+3x^3-10x^2-9$
(ii) $\sqrt{2x^5}\ +x\ -9$
(iii) $x^9+\frac{3}{5}x^{45}\ -\ \sqrt{3}.x\ -9$
(iv) $\frac{3}{x^2}+x^3\ +2$
manakah yang bukan termasuk polinomial

a)

( i ) dan ( ii )

b)

( i ) dan ( iii )

c)

( iii ) dan ( v)

d)

( ii ) dan ( iii )

e)

( iii) dan ( iv )

67.

Does this function have an absolute maximum?

a)

Yes

b)

No

68.

How many relative extrema are in the picture?

a)

2

b)

3

c)

4

d)

5

69.

Does this graph have an absolute minimum?

a)

Yes

b)

No

70.

Which of the following are power functions?

a)

b)

c)

d)

Both option 1 and option 3 are power functions.

71.

The function shown has:

a)

Degree two with negative leading coefficient.

b)

Degree three with negative leading coefficient.

c)

Degree four with negative leading coefficient.

d)

Degree four with positive leading coefficient.

72.

Which of the following could be a possible equation for the function shown?

a)

f(x) =-2x³ + x² - 5x + 1

b)

f(x) = 2x³ - 4x² + x + 1

c)

f(x) = 3x² + 5x + 1

d)

f(x) = -2x³ +3x - 1

73.

State the minimum degree of the function shown:

a)

3

b)

4

c)

5

d)

6

74.

Select all the graphs which show even degree functions.

a)

b)

c)

d)

75.

Which of the following functions contain line symmetry?

a)

g(x) = 3x³ + 2x²

b)

g(x) = 5x⁴ + 3x³ + 4x²

c)

g(x) = 3x⁶

d)

g(x) = 18x³

76.

Which of the following functions could represent the graph shown?

a)

f(x) = -2x⁵

b)

f(x) = -2x⁴ + 7x³ + 3x² -5x + 8

c)

f(x) = 2x⁵ + 3x⁴ - 3x³ + 5x² - 3x + 4

d)

None of these functions could represent the graph shown.

77.

Which description best matches the function shown:

a)

Odd degree with positive leading coefficient.

b)

Even degree with positive leading coefficient.

c)

Degree three, with negative leading coefficient.

d)

Degree four, with negative leading coefficient.

78.

The function f(x) = -5x⁴ + 3x² - 3x + 5

a)

Extends from quadrant 2 to quadrant 1.

b)

Extends from quadrant 2 to quadrant 4.

c)

Extends from quadrant 3 to quadrant 1.

d)

Extends from quadrant 3 to quadrant 4.

79.

The function shown contains:

a)

Only one local maximum.

b)

Two local maximums.

c)

Two local minimums.

d)

Three local maximums

80.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

81.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

82.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

83.

Which of the following correctly identifies the End Behavior?

a)

b)

c)

d)

84.

What are the decreasing interval(s)?

a)

(- ∞, 0) & (2, ∞ )

b)

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

c)

(0,2)

d)

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

85.

Is the leading coefficient positive or negative

a)

positive

b)

negative

86.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

87.

If a zero of a polynomial function has multiplicity 4 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

88.

What is the minimum of this graph?

a)

2

b)

4

c)

-3

d)

-1

89.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

90.

What are the increasing intervals?

a)

(- ∞, -1) & (-1, 0) & (0, 1) & (1, ∞)

b)

(3, 4) & (3, 8)

c)

(- ∞, -1) & (1, ∞)

d)

(-1, 0) & (1, ∞)

91.

Which graphs are polynomials?

a)

b)

c)

d)

92.

Which graphs are polynomials?

a)

b)

c)

d)

93.

Which functions are polynomials?

a)

$y=6x^2-1$

b)

$y=\log\left(x\right)$

c)

$y=x^3+2x^2+x$

d)

$y=x$

94.

Which functions are polynomials?

a)

$y=4x^5$

b)

$y=x^3-2x+1$

c)

$y=x^2+x^{-1}$

d)

$y=2^x$

95.

Which functions is a polynomial?

a)

$y=\left|x-4\right|$

b)

$y=x-4$

c)

$y=\frac{1}{x-4}$

d)

$y=\sqrt{x-4}$

Polinomi - banka nalog

Total questions: 95

Worksheet time: 5hrs 30mins

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