Polynomials

Exponent Rules

100

Simplify

4p² * 5p³

20p⁵

200

Simplify

(-2y³)^-4

1 ÷ 16y¹²

300

Simplify

(4xy ÷ 5x³)²

16y² ÷ 25x⁴

400

Simplify

(3xyz⁰)(6x^-2y)²

108y³ ÷ x³

500

Simplify

(5x^-2y)^-3(5xy³)⁴ ÷ xy

5y⁸ ÷ x³

Adding, Subtracting, Multiplying, Dividing

100

(x⁴+5X³-2X+6) + (5X³-3X+1)

X⁴+5X³+3X²-5X+7

200

(x³+3x²-7x+5) - (3x³-4x²+9x-3)

-2x³+7x²-16x+8

300

Multiply

(x²-1) (x+7) (x-5)

x⁴+2x³-36x²-2x+35

400

Myltiply

(x²+1) (3x²+3x-1)

3x⁴+3x³+2x²+3x-1

500

Divide

2x³+x²-6x-8 ; x-2

2x²+5x+4

Factoring and Finding Zeros

100

Find the zeros

x²+2x+2

x= 1+i, 1-i

200

Factor Completely

x³+4x²-7x-10

(x+1) (x-2) (x+5)

300

Factor

x⁶+ 27x³

x³ (x+3) (x²-3x+9)

400

Find all the Zeros

6x⁴+9x³-24x²-36x

x= 0, -3/2, 2, -2

500

Factor

8x⁴+8x³+27x+27

(x+1) (2x+3) (4x²-6x+9)

Graphing

100

what is the degree, leading coefficient and number of solutions of this polynomial?

x³-27

Degree: 3

Leading Coeffiecent: 1

# of solutions: 3

200

What is the degree, leading coefficient and number of solutions of this polynomial?

-7x³-4x²-3x+12

Degree: 3

Leading Coefficient: -7

# of solutions: 3

300

What is the degree, leading coefficeint and number of solutions of this polynomial?

5x⁴+7x²-8x+6

Degree: 4

Leading coefficient: 5

# of solutions: 4

400

What are the end behaviors of this polynomial?

x⁴-3x³+7x²+4x+9

as x -> + Infinity

     f(x) -> + Infinity

as x -> - Infinity

     f(x) -> + Infinity

500

What are the end behaviors of this polynomial?

-3x³+2x²-x+5

as x -> + Infinity

     f(x) -> - Infinity

as x -> - Infinity

     f(x) -> + Infinity

Using solutions to find the polynomial

100

x= 1, -3, -4

x³+6x²+5x-12

200

x= -5, 4, -3

x³+4x²-17x-60

300

x= 6i

x²+36

400

x= 4, 5i

x³-4x²+25x-100

500

x= 1-2i, 3

x³-5x²+11x-15