Polynomials and Factoring

Adding and Subtracting Polynomials

100

Simplify: (9x + 6x³ - 8x²) +(-5x³ + 6x)

What is x³ - 8x² + 15x

200

Simplify: (7a³ - 4a² - 2a + 1) + (a³ - 1)

What is 8a³ - 4a² - 2a

300

Simplify: (3n² - 4n + 1) - (8n² - 4n + 17)

What is -5n² - 16?

400

Simplify: (2s² + 8) - (-3s³ + 7s -5)

What is 5s³ - 7s + 13?

500

Simplify: (-k² + 7k + 5) - (2k⁴ - 3k³ - 6)

What is -2k⁴ + 3k³ - k² + 7k + 11

Multiplying Polynomials

100

Multiply: 3x² ( 3x² + 2x - 8)

What is 9x⁴ + 6x³ - 24x²

200

Multiply: (3s² + 5)(3s² - 5)

What is 9s⁴ - 25?

300

Multiply: (2a - 1)(a - 3)

What is 2a² - 7a + 3

400

Multiply: (6y + 1)²

What is 36y² + 12y + 1

500

Multiply: (x² - 2x + 1)(x - 3)

What is x³ - 5x² + 7x - 3?

DividingPolynomials

100

Divide: 12x²+24x³/6x²

2+4x

200

Simplify: (3x³ - 2x +5) divided by (x - 2)

3x²+6x +10 + 25/(x-2)

300

Divide: (x²-2x -35)/(x+5)

What x -7?

400

Divide: (x²+x-6)/(x²- 7x + 10)

(x+3)/(x-5)

500

Factor completely: 3x⁴y - 300x²y

What is 3x²y(x - 10)(x + 10)?

Factor Polynomials

100

Factor: n² +15n + 26

What is (n + 13)(n + 2)

200

Factor:b² - 5b - 14

What is (b - 7)(b + 2)

300

Factor: 25z² - 49

What is (5z -7)(5z + 7)?

400

Factor: 2a⁴ + 21a³ + 49a²

What is a²(2a + 7)(a + 7)?

500

Factor: -7y² -23y - 6

What is -(7y + 2)(y + 3)?

Mixed Bag

100

Simplify: (y³x^-2)( y^-5x²)

What is 1/y²?

200

Factor: -3y² + 36y - 108

What is -3(y - 6)²

300

Simplify: (3x²y^-2)²

9x⁴/y⁴

400

Factor: n³ - m³

What is (n - m) ( n² + nm +m²)?

500

Simplify: -4²(-3x^-2y³)⁰

What is -16?