Polynomials and Polynomial Functions

Polynomials Operations

100

(t² + 3t³ -3) + (2t² +7t -2t³)

t³ +3t² +7t -3

200

(-x² - 5) - (-3x² -x -8)

2x² + x +3

300

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

400

Simplify: 

(x+7)³ 

x³+21x²+147x+343

500

(3x²+2x-7)(5x²-6x)

15x⁴-8x³-47x²+42x

End Behavior

100

Describe the end behavior of the function: y = x²

as x→−∞, f(x)→+∞

 as x→+∞, f(x)→+∞

200

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

as x→−∞, f(x)→+∞

 as x→+∞, f(x)→-∞

300

Describe the end behavior of the function: y = -3x⁶ + 4x⁵ + 1

as x→−∞, f(x)→-∞

 as x→+∞, f(x)→-∞

400

Describe the end behavior of the function: y = 7x³ - 2x⁵ - 10x + 9

as x→−∞, f(x)→+∞

 as x→+∞, f(x)→-∞

500

Describe the end behavior of the function  y = 7x⁷ - 5x⁸ + 8x³-6x²+25

as x→−∞, f(x)→-∞

 as x→+∞, f(x)→-∞

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 factored form with the given zeros: 1, -1, -2i

y = (x+1)(x-1)(x²+4)

Solving Polynomial Equations

100

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

{2, 6}

200

Find the other solutions of x⁴-2x³+3x²-24x-180 given a zero of 5

{5,3, i√ 12, -i√ 12}

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