Operations with Polynomials and Cubic Functions Review

Standard Form and Function Composition

100

Rewrite in Standard Form:

-6a⁴ + 10a³ + 14a⁷ - 22a² + 33

14a⁷ - 6a⁴ + 10a³ -22a² +33

200

Rewrite in Standard Form:

5a² - 6a - 6a⁴ - 6a⁹ - 5a⁷

-6a⁹ - 5a⁷ - 6a⁴ + 5a² - 6a

300

Perform the indicated operations using 

f(x)=x²-2x+1 and g(x)=3x-7

f(g(1))=?

f(g(1))=25

400

Combine like terms and write in Standard Form:

4x - 9x² + 4x³ - 5x⁴ +11 - 4x³ -3x² - 8x + 4x²

-5x⁴ - 8x² - 4x + 11

500

Perform the indicated operations using 

f(x)=x²-2x+1 and g(x)=3x-7

g(f(x))=?

g(f(x))=3x²-6x-4

Adding Polynomials

100

Add the Polynomials:

(4x + 9) +(x - 4)

5x + 5

200

Add the polynomials:

(-3x - 2) + (7x + 5)

4x + 3

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(x² + 3x³ -3) + (2x² +7x -2x³) 

x³ +3x² +7x -3

500

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Subtracting Polynomials

100

Subtract the polynomials:

(x - 4) - (3x - 6)

-2x + 2

200

Subtract the polynomials:

(-5x - 2) - (7x +6)

-12x - 8

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(x² + 6x³ -4) - (5x³ + 7x -3x²)

x³ + 4x² -7x -4

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴+4x²-5)

6x⁶+12x⁴-15x²

200

Multiply the Polynomials:

(2x+1)(3x-4)

6x²-5x-4

300

Multiply the Polynomials:

(x²+4)(2x-7)

2x³-7x²+8x-28

400

Multiply the Polynomials:

(x-3)(x²+2x-4)

x³-x²-10x+12

500

Multiply and name the Polynomial

(x²+5x-3)(2x²-3x+1)

2x⁴+7x³-20x²+14x-3

Quartic Polynomial

Name Polynomials

100

5a² - 6a - 6a⁴ 

Quartic trinomial

200

1

constant monomial

300

4x - 9x² + 4x³  +11

Cubic 4 term polynomial

400

-4x³ + 4x³ - 33 + 4 + 9x⁵

^{hint: look closely at the number of terms after combining like terms}

Quintic binomial

500

(4x + 9) +(x - 4 + y)

Hint: look closely at the terms after completing the computation

Linear trinomial

Cubic Functions

100

State the transformations from the parent function y=x³:

y=-(x+1)³-5

reflected, shifted left 1 and down 5

200

State the transformations from the parent function y=x³:

y=3/2(x-5)³+8

Stretched by 3/2, shifted right 5 and up 8

300

Write a possible equation for the function below:

(see google slide 1)

y=2(x-3)³+2

400

Write an equation of a cubic function that is stretched vertically by a factor of 7, reflected over the x-axis, shifted left 3 and down 9.

y=-7(x+3)³-9

500

Graph the following without making a table of values.  State the domain, range, x-intercept, and y-intercept.

y=-(x+1)³+8

(see google slide 2 for graph)

D: all real numbers

R: all real numbers

x-int: (1,0)

y-int: (0,7)