Unit 3: Polynomial Functions

Naming Polynomials

100

Write the name of the polynomial:

y=x²+3x-1

quadratic trinomial

200

Write the name of the polynomial:

y=4

constant monomial

300

Write the name of the polynomial:

y=4x³-2x²+x-1

cubic polynomial

400

Write the name of the polynomial:

y=10x¹⁰-x

10^th degree binomial

500

Write the name of the polynomial:

f(x)=x⁸+4x⁹-9x

9^th degree trinomial

Operations with Polynomials

100

Simplify the expression:

(2x²+4x)+(3x²-3x)

5x²+x

200

Simplify the expression:

(x³-2x+1)-(2x²-3)

x³-2x²-2x+4

300

Simplify the expression:

(4x²+2x)(x²+3x-4)

5x⁴+14x³-10x²-8x

400

Simplify the expression:

(x³+6x²+13x+10)/(x+2)

x²+4x+5

500

Simplify the expression:

(2x²+7x-4)/(x-3)

2x+13+(35/x-3)

Solving Polynomials

100

Find all solutions to the polynomial:

y=x²+7x+12

x = -3, -4

200

Find all solutions to the polynomial:

y=x³+3x²-16x-48

x = 4, -4, -3

300

Find all solutions to the polynomial:

y=2x³+x²+8x+4

x = (-1/2), 2i, -2i

400

Find all solutions to the polynomial:

y=x⁴-20x²+64

x = 4, -4, 2, -2

500

Find all solutions to the polynomial:

y=x⁸-17x⁴+16

x = 1, -1, i, -i, 2, -2, 2i, -2i

Writing Polynomials

100

Write a polynomial with the following roots:

x = 3, -4

y=x²-x-12

200

Write a polynomial with the following roots:

x = -2, -4, 5, 7

y = x⁴-6x³-29x²+114x+280

300

Write a polynomial with the following roots:

x = 2, 2i, -2i

y = x³-2x²-4x+8

400

Write a polynomial with the given roots:

x = 3 + 2i, 3, -4

y = x⁴-5x³-9x²+81x-108

500

Write a polynomial with the given roots:

x = -1, -2i, -3, -4i

y = x⁶+4x⁵-17x⁴-80x³+4x²+256x+192

Graphing Polynomials

100

Sketch a graph of the polynomial.  Include all x-intercepts, y-intercepts, and end behavior.

y = x²+5x+6

y-int: (0,6)

x-int: (-3,0) cross, (-2,0) cross

Even/Positive -> starts and ends positive

200

Sketch a graph of the polynomial.  Include all x-intercepts, y-intercepts, and end behavior.

y = x⁴-2x³+x²

y-int: (0,0)

x-int: (0,0) touch, (1,0) touch

Even/Positive -> starts and ends positive

300

Sketch a graph of the polynomial.  Include all x-intercepts, y-intercepts, and end behavior.

y = 6x⁵+4x⁴-9x-36

y-int: (0,-36)

x-int: (-4,0) cross, (sqrt(3),0) cross, (-sqrt(3),0) cross

Odd/Positive -> start negative end positive

400

Sketch a graph of the polynomial.  Include all y-intercepts, x-intercepts, and end behavior.

y=x⁸-8x⁴+16

y-int: (0, 16)

x-int: (sqrt(2), 0) touch, (-sqrt(2), 0) touch

Even/Positive -> start and end positive

500

Sketch a graph of the polynomial.  Include all y-intercepts, x-intercepts, and end behavior.

y=-x⁵

y-int: (0,0)

x-int: (0,0) cross

Odd/Negative -> start positive end negative