Polynomials

Polynomial Divison

100

(3x²+6x+9)/(x+2)

3x+6 remainder -3/(x+2)

200

(8x³+12x²+3x)/(x²-3)

8x+12 remainder 27x+36/(x²-3)

300

(2x²+2x+2)/(x+8)

2x-8 remainder 66/(x+8)

400

(20x⁴+10x³+5x²+2x+2)/(5x²+10)

4x²+2x-7 remainder -18x+72/(5x²+10)

500

(6x⁴+2x²+x)/(2x+3)

3x³-4.5x²+7.75x remainder -22.25x/(2x+3)

Polynomial Multiplication

100

(4x+3)(3x+9)

12x²+45x+27

200

(5x+6)(3x+4)

15x²+38x+24

300

(2x+5)(7x-10)

14x²+15x-50

400

(8x²+7)(6x+2)

48x³+18x²+42x+14

500

(3x²+2x+1)(4x+8)

12x³+32x²+20x+8

Polynomial Subtraction

100

(4x²+2x)-(2x²+4x)

2x²-2x

200

(6x³-7x)-(3x³+5x)

3x³-12x

300

(10x⁴+4x³+2x²)-(8x⁴+3x³+x²)

2x⁴+x³+x²

400

(24x³+8x²)-(27x³+5x²)

-3x³+3x²

500

(40x⁴+30x³+10x²+3x)-(20x⁴+10x³+5x²+2x)

20x⁴+20x³+5x²+x

Polynomial Addition

100

(5x³+3x²+x)+(10x³+7x²+3x)

15x³+10x²+4x

200

(10x³+5x²+3x)+(2x³+6x²+13x)

12x³+11x²+16x

300

(3x⁴+5x³+6x²+8x)+(2x⁴+7x³+10x²+17x)

5x⁴+12x³+16x²+25x

400

(7x⁴+9x³+15x²+7x)+(4x⁴+8x³+15x²+30x)

11x⁴+17x³+30x²+37x

500

(8x⁵+2.5x³+20x²+15x)+(x⁵+x³+5x²+2x)

9x⁵+3.5x³+25x²+17x

Rationalizing Denominator

100

2/(√2+3)

(-2√2+6)/7

200

4/(√6+7)

(-4√6+28)/43

300

6/(√10+4)

4-√10

400

√-7/(2+√-12)

(i√7-√21)/8

500

√-8/(6+√24)

(3i√2-2i√3)/3