CRM Unit 5 Polynomial Functions & Radicals

Polynomial Basics

100

What is the degree and leading coefficient of the following polynomial function?

2x⁸ - 14x³ + 22 - x⁹

Degree: 9

Leading Coefficient: -1

200

What is the degree and leading coefficient of the following function?

  x²- 12x + 14 - 3x³ + x³ - 7x²

Degree: 3

Leading Coefficient: -2

300

Rewrite the function in standard form and state its degree and leading coefficient:

17x - 19 + 2x + 8 + 4x²

Standard Form: 4x² + 19x -11

Degree: 2

Leading Coefficient: 4

400

Rewrite the function in standard form and state its degree and leading coefficient:

3x³ + 4 - 12x³ + x⁶ - 12 + x² - 4x⁶

Standard Form: -3x⁶ - 9x³ + x² - 8

Degree: 6

Leading Coefficient: -3

500

Rewrite the function in standard form and state its degree and leading coefficient:

6x¹⁰ - 17x + 2x² + x¹⁰ - 5x⁷ + 18 - 6x + 5

Standard Form: 7x¹⁰ - 5x⁷ + 2x² - 23x + 23

Degree: 10

Leading Coefficient: 7

Graphing Polynomials

100

What is the maximum number of turning points this function can have:

8x⁷ - 14x + 56

6

200

What is the maximum number of turning points this function can have:

3x - 26x² + x⁴ - 17x⁵ + 39

4

300

What is the end behavior of the following function: 

-2x¹⁸ - 7x³ - 22

As x-->negative infinity, y-->negative infinity

As x-->infinity, y-->negative infinity

400

What is the end behavior of the following function:

6x - 2x³ + 18 - 2x²

As x-->negative infinity, y-->infinity

As x-->infinity, y-->negative infinity

500

What is the end behavior of the following function:

5x⁸ + 2x⁸ + 16x⁴ - 12x⁷ - x⁸ + 3 - 4x + 19

As x-->negative infinity, y-->infinity

As x-->infinity, y-->infinity

Factoring Polynomials

100

Factor:

p² +2p -35

(p-5)(p+7)

200

Factor:

z² - 4z - 21

(z+3)(z-7)

300

Factor:

-5y² - 22y - 8

(-5y-2)(y+4)

400

Factor:

6v² + 66v + 60

6(v + 10)(v + 1)

500

Solve by factoring:

x² - 25=0

x=-5 and x=5

Finding Zeros

100

The possible rational roots of the following polynomial function f(x) = 2x³ - 2x² + x - 15.

-1, 1, -3, 3, -5, 5, -15, 15, -1/2, 1/2, -3/2, 3/2, -5/2, 5/2, -15/2, 15/2

200

The zeros of the function f(x) = x³ + 7x² + 10x.

{0, -2, -5}

300

Is (x-2) a factor of P(x) = x³ + 2x² -6x - 4?

Yes; P(x) = (x - 2)(x2 + 4x + 2).

400

The zeros of the function f(x) = x⁴ - 40x² + 144.

{-6, -2, 2, 6}

500

Find the zeros of  f(x)? 

f(x)=5x²+17x−12

x=3/5 or x=−4

Solving & Graphing Radicals

100

Solve for x √(2x + 6) = 6

x = 15

200

Solve for x √(3x - 1) = √(2x + 5)

x = 6

300

Solve for x:   √(x + 7) = x + 1

x = 2

400

What is the starting point and end behavior of the function f(x)=√x−7 ?

(0, 7)

x --> positive infinity, y --> positive infinity

500

What is the starting point and end behavior of the function f(x)=-√(x+2)+3 ?

(-2, 3)

x--> positive infinity, y --> negative infinity