Free Printable Finding zeros

Worksheets

Finding zeros

Total questions: 35

Worksheet time: 3hrs 53mins

Name

Class

Date

Write the polynomial in factored form.

x(x-4)(x+3)=0

2(x-4)(x+3)=0

Find the zeros by factoring

x=0

x=2 and x=-6

x=0, x=-4 and x=6

x=0, x=2 and x=-6

What are the solutions? (Hint Factor and solve)

x=0, x=-2 and x=7

x=2 and x=7

x=-2 and x=7

x=0 and x=3 and x= 42

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

x = 5, (2/3), 6, (7/4)

x= -5, (3/2), (-4/7), 6

x= 5, (-3/2), (4/7), -6

x= 6, 5, -2/3, -4/7

Write a polynomial in factored form with zeros at x = 1, x = -1 x = 0

(x - 1)(x + 1)

x(x - 1)(x + 1)

x²(x - 1)(x + 1)

x(x - 1)(x - 1)

Identify the degree of the polynomial and the sign of the leading coefficient, using the graph.

Leading Coefficient Positive
Degree - Even

Leading Coefficient Positive
Degree - Odd

Leading Coefficient Negative
Degree - Even

Leading Coefficient Negative
Degree - Odd

What are the zeros of the function?

4,1

3,1,-2,-5

-3, -1, 2, 5

-2,4

10.

Identify the zeros

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

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

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

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

11.

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

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

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

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

x = 4, x = 3, x = 2

12.

Find the ACTUAL rational zeros

13.

What is the factor associated with a zero of 5

-5

x - 5

x + 5

14.

Write the polynomial with the given zeros

15.

If polynomial P(x) is divided by ( 2x - 5 ), with a remainder of -2, is ( 2x - 5 ) a factor of P(x)?

yes

16.

Use long division algorithm.

7x - 2

7x + 2

2x - 7

2x + 7

17.

Identify the missing term to complete the solution.

18.

Identify the missing term to complete the solution.

-2

-3

19.

Is this division problem worked correctly?

This is correct!

This is incorrect!

20.

Divide (x² + 5x - 8) by (x + 3). What is the remainder?

-14

-16

21.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

22.

Which term is missing in this problem?

(2x³ + 5x² + 9) ÷

(x + 3)

x⁴

x³

x²

23.

For synthetic division, what would be the number in the left hand box?

-2

24.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

3 0 -4 6 1

6 -4 3 1 0

6 -4 0 3 1

-6 4 0 -3 -1

25.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

2x³ - x² + x + 9

2x² - x + 1

2x² - x + 1 + 9/x-2

2x² - 9x - 15 - 23/x-2

26.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Yes

27.

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

-1,-3,-3

-1,-3,3/2

3,3,3

-3,2/3,-1

28.

Find all rational zeros, one zero has been given.
f(x) = x³-5x²-2x+24; -2

-2,1,0

-2,-3,-4

4,3,-2

0,0,0

29.

One zero of 3x³-4x²-28x-16 is 4.
What is another zero?

-2

30.

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

P(x) = x³+2x²+9x+11

P(x) = x³-2x²+9x+18

P(x) = x³+2x²+9x+18

P(x) = x²-3ix+2x-6i

31.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

32.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

-2, 7 multiplicity 3

-2, 7, 3

2, -7 multiplicity 3

2, -7, 3

33.

f(x)= x²(x – 2)³(x – 7)

State the zeros, include multiplicity.

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

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

0, 2, 7

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

34.

Choose the correct equation

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

y = x(x-3)²(x+2)

y = x(x+3)²(x-2)

y = -x(x+3)²(x-2)

35.

Find all zeros of the polynomial function P(x) = x³+6x²+9x+54

6, 3, -3

-6, 3, -3

-6, 3i, -3i

6, 3i, -3i

100 %

Finding zeros

Total questions: 35

Worksheet time: 3hrs 53mins

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