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/SubtractingPolynomials

100

Add the Polynomials:

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

5x + 5

200

Add the polynomials:

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

4x + 3

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

500

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

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

Solve by Factoring

100

x²-25=0

x = 5, -5

200

3x²-3x-60=0

x=-4, 5

300

5x²-40x=0

x = 0, 8

400

Factor by Grouping:

(3x²+2x) + (12x+8)

x= -4, -2/3

500

Factor by Grouping:

(x³-2x²)+(5x-10)

x=2, sqrt(-5)