Polynomials and Polynomial Functions

Multiplicity

100

What is the multiplicity of the zero at x = -3 for the function 

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

Multiplicity 2

200

What is the multiplicity of the zero at x = 0 for the function

f(x) = x^4(x-3)^3(6x+1)^7

Multiplicity 4

300

What is the multiplicity of the zero at x = 2 for the function

f(x) = x^4(x-2)^3(x+2)^7

Multiplicity 3

400

What is the total number of zeros for the function 

f(x) = x^4(x-2)^3(x+2)^7

14

500

What is the total number of zeros for the function 

f(x) = 3x^4 + 4x^7 -5x -1+7x^3

7

Polynomial Factors and Zeros

100

Find the zeros of the function: y = (x - 3)(x + 2)

{-2, 3}

200

Write the polynomial in factored form: x³ + 7x² + 10x

x(x + 5)(x + 2)

300

Find the zeros of the function: y = x(x + 1)(x - 7)

{-1, 0, 7}

400

Write a polynomial function in standard form with the given zeros: 5, 4

y = x² - 9x + 20

500

Write a polynomial function in standard form with the given zeros: 1, -1, -2

y = x³ + 2x² - x - 2

Solving Polynomial Equations

100

Find all real solutions of the polynomial equation: x² - 25 = 0

{-5, 5}

200

Find all real solutions of the polynomial equation: x² - 8x = -12

{2, 6}

300

Find all real solutions of the polynomial equation: x³ - 3x² - 4x = 0

{-1, 0, 4}

400

Find all real solutions of the polynomial equation: x³ - 15x² = -14x

{0, 1, 14}

500

Find all real solutions of the polynomial equation: x³ - 4x² - 6x +24= 0

{4, sqrt6, -sqrt6}

Dividing Polynomials

100

Find the remainder: 347 ÷ 16

11

200

Find the quotient: (x² + 10x + 21) ÷ (x + 3)

x + 7

300

Find the quotient and remainder: (2x² + 7x + 8) ÷ (x + 2)

Quotient: 2x + 3, remainder: 2

400

Find the quotient and remainder: (x³ + 3x² - x + 2) ÷ (x - 1)

Quotient: x² + 4x + 3, remainder: 5

500

Find the quotient and remainder: (x³ + 11x + 12) ÷ (x + 3)

Quotient: x² - 3x + 20, remainder: -48