Thomas Unit 2 Review - Operations with Polynomials

Combining Functions

100

f(x)= 16x² + 8x - y + z

g(x)= -z + y - 8x - 16x²

Find  f(x) + g(x)

f(x) + g(x) = 0

200

f(x)= 9x⁴ + 18x³ - 9y + 1

g(x)= -8x³ + x -9

Find  f(x) - g(x)

f(x) - g(x) = 9x⁴ + 26x³ - x - 9y + 10

300

f(x)= 2x + 1

g(x)= x² - x + 5 

Find  f(x) - g(x)

h(x) = - x² + 3x - 4

400

Given that: 

 f(x) = 2x²  3x - 6   and  g(x) = x³ -2x + 1  

a. What type of function would result in adding

Cubic

500

h(x) = f(x) / g(x)

f(x) = 6x³ -22x² -80x -24

g(x) = 2x + 4

h(x) = 3x² - 17x -6

Composition of Functions

100

Find e(f(6))

e(x) = -2x + 1

f(x) = x² -10

e(f(6)) = -51

200

f(x)= 3x + 7

g(x)= x³ + 1

Find  f(g(3))

f(g(3)) = 91

300

f(x)= x² - 10 

d(x)= 4x³

Find  f(d(4))

f(d(4)) = 864

400

f(x) = x² - 2x + 1

g(x) = x - 5

Find f(g(2))

f(g(2)) = 16

500

f(x) = -2x + 4

g(x) = 2x² - x + 20 

Find g(f(-2))

g(f(-2)) = 128

Vocabulary

100

What letter represent the input values

X's

200

What function has an exponent with a power of 2

Quadratic 

300

Define Composite function

A function that takes the output of one function and uses it as the input of another function.

400

Define Combined functions

The result of adding, subtracting, multiplying and/or dividing two or more functions. 

500

Does the output values represent the domain or the range?

Range

Multiplying of polynomials

100

h(x) = f(x) * g(x) 

f(x) = 2x - 5

g(x) = 3x² + x - 4

h(x) = 6x³ - 13x² -13x + 20

200

Find h(x) = f(x) * g(x)

f(x) = 2x + 6

g(x) = x - 5

h(x) = 2x² - 4x - 30 

Division of Polynomials

100

How do you know a function is a factor of another function using synthetic or long division?

The remainder, R, is 0

200

Use synthetic or long division to solve the following:

(x³ – 2x + 1) / (x – 1)

x² + x – 1

300

What is the remainder, R, of the following problem?

(4x³ – 10x² – 11x + 16) / (x – 4)

68

400

Use synthetic or long division to solve the following:

(12x³ - 11x² + 9x + 18) / (4x + 3)

3x² - 5x + 6

500

f(x)= 2a³b²c - 4a²bc + 6a⁴b²c²

g(x)= 2a²bc

Find  f(x) / g(x)

f(x) / g(x) = ab - 2 + 3a²bc