Polynomials and Polynomial Functions

Classifying Polynomials

100

Write the polynomial in standard form: 3 - 4x³ + 2x²

- 4x³ + 2x² + 3

200

Classify the polynomial by number of terms (provide the name): x³ + 2

Binomial

300

Classify the polynomial by degree (provide the name): 5x² - 3x + 12

Quadratic

400

Classify the polynomial by degree and number of terms (provide the names): -2x⁴

Quartic monomial

500

Write in standard form, then classify the polynomial by degree and number of terms (provide the names): 3x³ + 8 - x³ - 7x²

2x³ - 7x² + 8; cubic trinomial

Random

100

Where is Ms. Myers currently, and what is she doing. 

In Canada mountain biking for her honey moon. She misses you guys too! 

200

How many solutions will x³+3x=y have?

3 solutions

300

Is this parabola reflected or not?

What is the y-intercept as a coordinate pair?

y = -3x² + 4x + 1

reflected and (0,1)

400

Simplify fully: 

2x(3x-4)-(x²-4)+3x

5x²-x

500

Fully Simplify

y = -3-4(7x - 5x² + 8x)-7

5x²-60x-10

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 = 0

{0, 2 + √10, 2 - √10}

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