Polynomials and Polynomial Functions

Graphs of Polynomials

100

Sketch a graph of a polynomial that:

- Crosses the x-axis only at x=4,5, and 10

Wait for Ms. Shute to check.

200

Sketch a graph of a polynomial that:

- Crosses the x-axis only at x=4,5, and 10

- Bounces at x=4 and x=10

Wait for Ms. Shute to check.

300

Sketch a graph of a polynomial that:

- Crosses the x-axis only at x=4,5, and 10

- Bounces at x=4 and x=10

- Has an odd degree and falls to the right, rises to the left.

Wait for Ms. Shute to Check

400

Is it possible to have a polynomial that has an odd degree, rises to the left and falls to the right, and three factors that all have a multiplicity of 2?

No

500

Is it possible to have a graph with 5 factors, each with an even multiplicity, to rise to the left and rise to the right?

Yes

End Behavior

100

Describe the end behavior of the function: y = x²

Up, up

200

Describe the end behavior of the function: y = -x³

Up, down

300

Describe the end behavior of the function: y = -3x² + 4x + 1

Down, down

400

Describe the end behavior of the function: y = 7x³ + 2x² - 10x + 9

Down, up

500

Describe the end behavior of the function and find the y-intercept: y = 7x - 5x² + 8x

Down, down; (0,0)

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 the solutions of the polynomial equation: (x+2)(2x²+3x-9)=0

{-2, 3/2, -3}

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