Factoring & Solving Polynomials

Addition

100

(x² + 4x +2) + (3x - 7)

x² + 7x - 5

200

(3x² - x + 6) + (2x² + 5x - 3)

5x² + 4x + 3

300

(5x⁴ + 2x² - 8) + (3x⁴ - x³ + 7x)

8x⁴ - x³ + 2x² + 7x - 8

400

(4x³ - 2x² +7x - 9) + (3x³ + 5x - 4)

7x³ - 2x² +12x - 13

500

(6x³y - 4xy² + 7) + (3x³y + 9xy² - 5)

9x³y + 5xy² + 2

Subtraction

100

(4x² + 2) - (3x² - 1) 

​​​​

x² + 3

200

(6x³ - 4x² + 9x - 12) - (2x³ + 7x² - 5x +3)

4x³ - 11x² + 14x - 15

300

(13x² - 6x⁵ - 2x) - ( -10x² - 11x⁵ + 9x)

5x⁵ + 23x² - 11x

400

(8n - 3n⁴ + 10n²) - (3n² + 11n⁴ - 7)

-14n⁴ + 5n² + 8n + 7

500

(9x⁵y - 4x³y² - 18) - ( -7x⁵y + 10x³y² + 25)

16x⁵y - 14x³y² - 43

Factoring

100

6x² + 17x + 12

(3x + 4)(2x + 3)

200

3x² + 4x - 4

(x + 2)(3x - 2)

300

4x⁴ - 9x² = 0 

x = 0, 3/2, -3/2

400

3x³ - 12x² + 9x = 0

x = 0, 1, 3

500

12x⁴ - 11x² - 5

(3x² - 5)(4x² + 1)

Multiplication

100

(x + 5)(x + 3)

x² + 8x + 15

200

(3x - 4)(x + 5)

3x² + 11x - 20

300

(3x - 1)(x² + 2x + 5)

3x³ + 5x² + 13x - 5

400

(2x - 5)(x³ + 4x² - x)

2x⁴ + 3x³ - 22x² + 5x

500

(x² + 3x + 1)(2x² - x + 4)

2x⁴ + 5x³ + 11x² + x + 4

Division

100

6x² + 12x / 3x

2x + 4

200

9x³ - 6x² + 15x / 3x

3x² - 2x + 5

300

x² + 7x + 10 / x + 2

x + 5

400

3x² - 5x - 12 / x - 3

3x + 4

500

4x² + x - 10 / x + 2 

4x - 7 + 4/x-2