Polynomials and Polynomial Functions

Degree & Lead Coefficient

100

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

- 4x³ + 2x² + 3

200

Find the degree of: x³ + 2

3 (odd)

300

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

Quadratic

400

Identify the degree and lead coefficient of: -2x⁴

Degree: 4 (even)

LC: -2 (negative)

500

Write in standard form, then classify the polynomial by degree (provide the name) and the identify the lead coefficient: 3x³ + 8 - x³ - 7x²

2x³ - 7x² + 8; cubic (degree 3, odd)

LC: 2 (positive)

End Behavior

100

Describe the end behavior of the function: y = x²

As x approaches positive infinity, f(x) approaches positive infinity.

As x approaches negative infinity, f(x) approaches positive infinity.

200

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

As x approaches positive infinity, f(x) approaches positive infinity.

As x approaches negative infinity, f(x) approaches negative infinity.

300

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

As x approaches positive infinity, f(x) approaches negative infinity.

As x approaches negative infinity, f(x) approaches negative infinity.

400

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

As x approaches positive infinity, f(x) approaches negative infinity.

As x approaches negative infinity, f(x) approaches positive infinity.

500

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

As x approaches positive infinity, f(x) approaches negative infinity.

As x approaches negative infinity, f(x) approaches negative infinity.

y-intercept: (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 and non-real solutions of the polynomial equation: (x+5)(x²+3x+7)

Real: -5

Non-real: (-3+i√19)/2 and (-3-i√19)/2

500

Find all real and non-real solutions of the polynomial function: x³-125 

Real: 5

Non-Real: (-5+5i√3)/2 and (-5-5i√3)/2

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