Writing Polynomials from Zeros

Question 1

Use the graph of f, a polynomial of least degree with leading coefficient 1. What is f in factored form?

Accepted Answer

f(x) = (x - 2)(x - 3)(x - 8)

Answer

f(x) = (x + 2)(x + 3)(x + 8)

Answer

f(x) = (x - 2)(x - 3)(x - 8)^2

Answer

f(x) = x(x - 2)(x - 3)(x - 8)

Question 2

The graph shows a degree-3 polynomial function with leading coefficient 1. What is its factored form?

Accepted Answer

f(x) = (x + 2)^2(x + 4)

Answer

f(x) = (x - 2)^2(x - 4)

Answer

f(x) = (x + 2)^2(x + 4)^2

Answer

f(x) = (x + 2)(x + 4)^2

Question 3

Use the graph of the quadratic function f, which passes through the marked point. What is f in factored form?

Accepted Answer

f(x) = 5(x + 4)(x - 4)

Answer

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

Answer

f(x) = 45(x + 4)(x - 4)

Answer

f(x) = -5(x + 4)(x - 4)

Question 4

A polynomial function with real coefficients has least degree and has 1 and 2 + 2i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 5x^2 + 12x - 8

Answer

f(x) = x^3 - 5x^2 + 4x

Answer

f(x) = x^3 - 3x^2 + 4x + 8

Answer

f(x) = x^3 + 3x^2 + 4x - 8

Question 5

Use the graph of the quadratic function f, which passes through the marked point. What is f in factored form?

Accepted Answer

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

Answer

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

Answer

f(x) = 24(x - 3)(x - 2)

Answer

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

Question 6

A polynomial function with real coefficients has least degree and has 4 and -1 + 2i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 2x^2 - 3x - 20

Answer

f(x) = x^3 - 2x^2 - 11x + 12

Answer

f(x) = x^3 + 6x^2 + 13x + 20

Answer

f(x) = x^3 - 6x^2 + 13x - 20

Question 7

Write a degree-3 polynomial function with leading coefficient 1 whose only zeros are -5 with multiplicity 2 and -4 with multiplicity 1. Give the answer in factored form.

Accepted Answer

f(x) = (x + 5)^2(x + 4)

Answer

f(x) = (x - 5)^2(x - 4)

Answer

f(x) = (x + 5)^2(x + 4)^2

Answer

f(x) = (x + 5)(x + 4)^2

Question 8

A polynomial function with rational coefficients has least degree and has 2 and 2 + 3 among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 6x^2 + 9x - 2

Answer

f(x) = x^3 - 6x^2 + 15x - 14

Answer

f(x) = x^3 - 2x^2 - 7x + 2

Answer

f(x) = x^3 + 2x^2 - 7x - 2

Question 9

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -6, 3 and 4. Give the answer in factored form.

Accepted Answer

f(x) = (x + 6)(x - 3)(x - 4)

Answer

f(x) = (x - 6)(x + 3)(x + 4)

Answer

f(x) = (x + 6)(x - 3)(x - 4)^2

Answer

f(x) = x(x + 6)(x - 3)(x - 4)

Question 10

The graph shows a degree-3 polynomial function with leading coefficient 1. What is its factored form?

Accepted Answer

f(x) = (x - 3)^2(x + 1)

Answer

f(x) = (x + 3)^2(x - 1)

Answer

f(x) = (x - 3)^2(x + 1)^2

Answer

f(x) = (x - 3)(x + 1)^2

Question 11

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are 4, 1 and 6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - 11x^2 + 34x - 24

Answer

f(x) = x^3 + 11x^2 + 34x + 24

Answer

f(x) = x^3 - 11x^2 - 34x - 24

Answer

f(x) = x^3 - 11x^2 + 34x + 24

Question 12

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, 1 and 6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - 4x^2 - 15x + 18

Answer

f(x) = x^3 + 4x^2 - 15x - 18

Answer

f(x) = x^3 - 4x^2 + 15x + 18

Answer

f(x) = x^3 - 4x^2 - 15x - 18

Question 13

Write a degree-4 polynomial function with leading coefficient 1 whose only zeros are 6 with multiplicity 3 and -4 with multiplicity 1. Give the answer in factored form.

Accepted Answer

f(x) = (x - 6)^3(x + 4)

Answer

f(x) = (x + 6)^3(x - 4)

Answer

f(x) = (x - 6)^3(x + 4)^3

Answer

f(x) = (x - 6)(x + 4)^3

Question 14

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -5, -2 and -6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 + 13x^2 + 52x + 60

Answer

f(x) = x^3 - 13x^2 + 52x - 60

Answer

f(x) = x^3 + 13x^2 - 52x + 60

Answer

f(x) = x^3 + 13x^2 + 52x - 60

Question 15

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -5, 1 and 5. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - x^2 - 25x + 25

Answer

f(x) = x^3 + x^2 - 25x - 25

Answer

f(x) = x^3 - x^2 + 25x + 25

Answer

f(x) = x^3 - x^2 - 25x - 25

Question 16

A polynomial function with real coefficients has least degree and has -1 and 1 + 2i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - x^2 + 3x + 5

Answer

f(x) = x^3 - x^2 - 5x - 3

Answer

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

Answer

f(x) = x^3 + 3x^2 + 7x + 5

Question 17

The graph shows a degree-4 polynomial function with leading coefficient 1. What is its factored form?

Accepted Answer

f(x) = (x - 6)^3(x - 1)

Answer

f(x) = (x + 6)^3(x + 1)

Answer

f(x) = (x - 6)^3(x - 1)^3

Answer

f(x) = (x - 6)(x - 1)^3

Question 18

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, 3 and 6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - 6x^2 - 9x + 54

Answer

f(x) = x^3 + 6x^2 - 9x - 54

Answer

f(x) = x^3 - 6x^2 + 9x + 54

Answer

f(x) = x^3 - 6x^2 - 9x - 54

Question 19

Use the graph of the quadratic function f, which passes through the marked point. What is f in factored form?

Accepted Answer

f(x) = 2(x - 1)(x + 5)

Answer

f(x) = (x - 1)(x + 5)

Answer

f(x) = -10(x - 1)(x + 5)

Answer

f(x) = 2(x + 1)(x - 5)

Question 20

Use the graph of f, a polynomial of least degree with leading coefficient 1. What is f in factored form?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, -2 and 4. Give the answer in factored form.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

Use the graph of f, a polynomial of least degree with leading coefficient 1. What is f in factored form?

Accepted Answer

f(x) = (x + 1)(x - 3)(x - 8)

Answer

f(x) = (x - 1)(x + 3)(x + 8)

Answer

f(x) = (x + 1)(x - 3)(x - 8)^2

Answer

f(x) = x(x + 1)(x - 3)(x - 8)

Question 23

A polynomial function with rational coefficients has least degree and has 4 and -3 + 6 among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 + 2x^2 - 21x - 12

Answer

f(x) = x^3 + 2x^2 - 9x - 60

Answer

f(x) = x^3 + 10x^2 + 27x + 12

Answer

f(x) = x^3 - 10x^2 + 27x - 12

Question 24

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, -4 and -6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 + 13x^2 + 54x + 72

Answer

f(x) = x^3 - 13x^2 + 54x - 72

Answer

f(x) = x^3 + 13x^2 - 54x + 72

Answer

f(x) = x^3 + 13x^2 + 54x - 72

Question 25

Write a degree-4 polynomial function with leading coefficient 1 whose only zeros are 6 with multiplicity 3 and 5 with multiplicity 1. Give the answer in factored form.

Accepted Answer

f(x) = (x - 6)^3(x - 5)

Answer

f(x) = (x + 6)^3(x + 5)

Answer

f(x) = (x - 6)^3(x - 5)^3

Answer

f(x) = (x - 6)(x - 5)^3

Question 26

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -4, -5 and -7. Give the answer in factored form.

Accepted Answer

f(x) = (x + 4)(x + 5)(x + 7)

Answer

f(x) = (x - 4)(x - 5)(x - 7)

Answer

f(x) = (x + 4)(x + 5)(x + 7)^2

Answer

f(x) = x(x + 4)(x + 5)(x + 7)

Question 27

A polynomial function with real coefficients has least degree and has 1 and 1 + 3i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 3x^2 + 12x - 10

Answer

f(x) = x^3 - 3x^2 - 6x + 8

Answer

f(x) = x^3 - x^2 + 8x + 10

Answer

f(x) = x^3 + x^2 + 8x - 10

Question 28

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -1, 3 and -6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 + 4x^2 - 15x - 18

Answer

f(x) = x^3 - 4x^2 - 15x + 18

Answer

f(x) = x^3 + 4x^2 + 15x - 18

Answer

f(x) = x^3 + 4x^2 - 15x + 18

Question 29

A polynomial function with rational coefficients has least degree and has 1 and -3 + 3 among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 + 5x^2 - 6

Answer

f(x) = x^3 + 5x^2 + 6x - 12

Answer

f(x) = x^3 + 7x^2 + 12x + 6

Answer

f(x) = x^3 - 7x^2 + 12x - 6

Question 30

Use the graph of f, a polynomial of least degree with leading coefficient 1. What is f in factored form?

Accepted Answer

f(x) = (x + 3)(x - 3)(x + 7)

Answer

f(x) = (x - 3)(x + 3)(x - 7)

Answer

f(x) = (x + 3)(x - 3)(x + 7)^2

Answer

f(x) = x(x + 3)(x - 3)(x + 7)

Question 31

Use the graph of the quadratic function f, which passes through the marked point. What is f in factored form?

Accepted Answer

f(x) = 5(x + 2)(x - 4)

Answer

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

Answer

f(x) = -40(x + 2)(x - 4)

Answer

f(x) = 5(x - 2)(x + 4)

Question 32

A polynomial function with real coefficients has least degree and has 1 and 3 + 2i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 7x^2 + 19x - 13

Answer

f(x) = x^3 - 7x^2 + 11x - 5

Answer

f(x) = x^3 - 5x^2 + 7x + 13

Answer

f(x) = x^3 + 5x^2 + 7x - 13

Question 33

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, -2 and 6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - x^2 - 24x - 36

Answer

f(x) = x^3 + x^2 - 24x + 36

Answer

f(x) = x^3 - x^2 + 24x - 36

Answer

f(x) = x^3 - x^2 - 24x + 36

Question 34

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -3, 3 and 4. Give the answer in factored form.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -5, -4 and -6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 + 15x^2 + 74x + 120

Answer

f(x) = x^3 - 15x^2 + 74x - 120

Answer

f(x) = x^3 + 15x^2 - 74x + 120

Answer

f(x) = x^3 + 15x^2 + 74x - 120

Question 36

A polynomial function with rational coefficients has least degree and has 1 and 2 + 6 among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 5x^2 + 2x + 2

Answer

f(x) = x^3 - 5x^2 + 14x - 10

Answer

f(x) = x^3 - 3x^2 - 6x - 2

Answer

f(x) = x^3 + 3x^2 - 6x + 2

Question 37

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are -5, 1 and 6. Give the answer in standard form.

Accepted Answer

f(x) = x^3 - 2x^2 - 29x + 30

Answer

f(x) = x^3 + 2x^2 - 29x - 30

Answer

f(x) = x^3 - 2x^2 + 29x + 30

Answer

f(x) = x^3 - 2x^2 - 29x - 30

Question 38

A polynomial function with real coefficients has least degree and has 2 and 3 + 3i among its zeros. Write it with leading coefficient 1, in standard form.

Accepted Answer

f(x) = x^3 - 8x^2 + 30x - 36

Answer

f(x) = x^3 - 8x^2 + 12x

Answer

f(x) = x^3 - 4x^2 + 6x + 36

Answer

f(x) = x^3 + 4x^2 + 6x - 36

Question 39

Use the graph of f, a polynomial of least degree with leading coefficient 1. What is f in factored form?

Accepted Answer

f(x) = (x - 5)(x - 3)(x - 4)

Answer

f(x) = (x + 5)(x + 3)(x + 4)

Answer

f(x) = (x - 5)(x - 3)(x - 4)^2

Answer

f(x) = x(x - 5)(x - 3)(x - 4)

Question 40

Write a polynomial function of least degree with leading coefficient 1 whose only zeros are 2, 3 and -7. Give the answer in factored form.

Accepted Answer

f(x) = (x - 2)(x - 3)(x + 7)

Answer

f(x) = (x + 2)(x + 3)(x - 7)

Answer

f(x) = (x - 2)(x - 3)(x + 7)^2

Answer

f(x) = x(x - 2)(x - 3)(x + 7)

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Writing Polynomials from Zeros

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Writing Polynomials from Zeros

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner