Polynomials

Polynomial Basics

100

Solve and simplify the polynomial.

2x² + 3x² + 3x + 4x  

5x² + 7x

200

-5x⁴ + 3x⁷ + 2x² + 3x² + 2

-5x⁴ + 3x⁷ + 5x² + 2

300

Name the type of polynomial that is listed below. 

-5x⁵ + 9x⁸ + 6x²

Polynomial Type: Trinomial

400

2x⁴ - 4x² - 9x³ + 7x² - 5x⁴

-3x⁴ - 9x³ + 3x²

500

-5x⁴ + 3x⁷ + 6x³ - 3x² - 2 + 7x - x + 4x⁴ + x³

Answer: -x⁴ + 3x⁷ + 7x³ - 3x² + 6x - 2

Multiplying Polynomials

100

(2m + 3)(4m + 5)

8m² + 22m + 15

200

(m+4)(4m+5)

4m² + 21m + 20

300

(2m+3)(6m-6)

12m² + 6m - 18

400

(2p+4)(2p² + 6p + 3)

4p³ + 20p² + 30p + 12

500

(x² + 3x - 2)(5x² + x + 7)

5x⁴ + 16x³ + 19x - 14

Quadratic Formula

100

x² + 5x + 6

(x+2)(x+3)

x = -2

x = -3

200

x² + 10x + 9

(x+1)(x+9)

x = -1

x = -9

300

2x² - 9x + 9

(x-6)(x-3)

x = 3

x = 6 

400

4x² + 28x + 40

4(x+2)(x+5)

x = -2

x = -5

500

2x² + 38x + 180

2(x+9)(x+10)

x = -9

x = -10

Variety Methods

100

x² + 9x + 20

(x+4)(x+5) 

200

x² - 10x - 24

(x - 12)(x + 2)

300

3x² + 13x + 10

(3x + 10) (x+1) 

400

2x² + 21x - 50

(2x + 25)(x - 2)

500

7x² + 19x + 10

(7x+5)(x+2) 

Factoring by Grouping

100

8r³ - 64r² + r - 8

(8r²+1)(r-8)

200

4v³ - 12v² - 5v + 15

(4v² -5)(v - 3)

300

49x³ - 35x² + 56x - 40

(7x² + 8)(7x - 5)

400

5a²z - 4a²c + 15xz - 12xc

(a² + 3x)(5z - 4c)

500

21xy - 12b² + 14xb - 18by

(7x - 6b)(3y + 2b)