Operations of Polynomials

Adding Polynomials

100

(4x² - 2) + (x² + 1)

5x² - 1 

200

(-2x³ + x² + 1) + (2x³ - x²)

1

300

(-x³ + x² - 4x + 6) + (-x³ - 5x² + x)

-2x³ - 4x² - 3x + 6

400

(5x + 4z + 2w) + (-5x - 4z - 2w)

0

500

(-10x⁵ - 9x⁴ +14x² + 3) + (-4x⁵ + 6x⁴ + x³ - 5)

-14x⁵ - 3x⁴ + x³ + 14x² - 2

Subtracting Polynomials

100

(5x² - 3) - (2x² + 1)

3x² - 4

200

(-3x³ + 2x² + 2) - (3x³ - 5x² + 2x)

-6x³ + 7x² - 2x + 2 

300

(-2x³ + 2x² - 5x) - (8x³ - 7x² + 5x)

-10x³ + 9x² - 10x

400

(-2x³ + 2x² - 5x + 7) - (-2x² - 13x³ - 3x + 4)

11x³ + 4x² - 2x + 3

500

(-11x⁵ - 8x⁴ + 15x² + 4) - (-5x⁵ + 7x⁴ + 2x³ - 6)

-6x⁵ - 15x⁴ - 2x³ + 15x² + 10

Type 1 and 2 Multiplication

100

8(-6x - 9)

-48x - 72

200

-3 (2x³ + 4x + 8)

-6x³ - 12x - 24

300

2x (-4x - 5x + 2)

-8x² - 10x + 4x

400

x² (2x⁵ - 6x⁶ + 3)

2x⁷ - 6x⁸ + 3x²

500

5x² (-3x³ - 2x + 16)

-15x⁵ + 10x³ + 80x²

Type 3 Multiplication

100

(x + 3) (x + 4)

x² + 7x + 12

200

(x - 8) (x - 10)

x² - 18x + 80

300

(x² - 13) (x + 1)

x³ + x² - 13x - 13 

400

(x³ - 5) (x² + 11) 

x⁵ + 11x³ - 5x² - 55 

500

(x² + 2x) (2x² - 5x)

2x⁴ - 6x³ - 10x² 

Type 4 Multiplication

100

(x - 12) (x - 9x + 2)

-8x² + 98x + 24 

200

(x² + 4) (5x² + 3x - 4)

5x⁴ + 3x³ + 16x² + 12x -16 

300

(3x² + 5x) (8x - 10 + 7x⁴) 

21x⁶ + 35x⁵ + 24x³ + 10x² - 50x 

400

(8x⁴ - 3x² + 2) (x² - 3x⁴ + 7) 

-24x⁸ + 17x⁶ + 47x⁴ - 19x² + 14 

500

(7x² - 6x - 6) (2x³ - 4 + 6x³ + 3)  

56x⁵ - 48x⁴ - 48x³ - 7x² + 6x + 6