Polynomial Functions

Rules of Exponents

100

Simplify: (3x²)³

What is 27x⁶

200

Simplify: (2y)(4xy³)

What is 8xy⁴

300

Simplify: 3x⁴y⁶(-8x³y

What is -24x⁷y⁷

400

Simplify: (3/5c²f)(4/3cd)²

What is 16/15c⁴d²f

Operations with Polynomials

100

Simplify: (4c-5)-(c+11)+(-6c+17)

What is -3c+1

200

Simplify: (d-5)(d+3)

What is d²-2d-15

300

(11x²+13x-15)-(7x²-9x+19)

What is 4x²+22x-34

Division of Polynomials

200

Simplify: (4x⁴-x³-19x²+11x-2)/(x-2)

What is 4x³+7x²-5x+1

300

Simplify: (x⁴+18x³+10x²+3x)/(x²+3x

What is x²+15x-35+108/(x+3)

400

The area of a triangular sail is 16x⁴-60x³-28x²+56x-32 square meters. The base of the triangle is x-4 meters. What is the height of the sail?

What is 16x³+4x²-12x+8

Analysis of Graphs

100

Make a table of values from -2 to 2 and determine where there is zeros of the graph. x⁴+7x+1

What is between -2 and -1, and between -1 and 0.

200

Create a table from -2 to 2 and find all relative max and mins. x³+x²-3x

rel max between -2 and 0, rel min between 0 and 2

300

Please look at the picture of the graph on the board. Please identify all relative mins/max, and zeros of the graph.

See answer on board.

Solving Polynomial Functions

100

Solve each equation by finding the zeros. x³-3x²-54x=0

What is x=-6,0,9

200

Solve the equation by find the zeros. x⁴-7x³+12x²

x=0,3,4

300

Solve the equation by finding the zeros. 10x³-20x²-2x+4=0

x=2, sqrt(1/5), -sqrt(1/5)