Polynomials

Addition

100

(3x²+7x-4) + (-2x²+8)

x²+7x+4

200

(4n + 5n³) + (3n + 2n²)

5n³ + 2n² + 7n

300

(12n³ + 14 + 13n⁴) + (8n³ + 7n⁴ + 11)

20n⁴ + 20n³ + 25

400

(6v⁵ + 12v⁴ + 4v²) + (7v² + 2v⁵ + v³)

8v⁵ + 12v⁴ + v³ + 11v²

500

(11xy⁴ - xy³) + (-1 + xy³ - 13x²) + (-4 + 14xy⁴)

25xy⁴ - 13x² -5

Subtraction

100

(b + 5b⁴) - (4b + b⁴)

4b⁴ - 3b

200

(m² + 2m⁴) - (m + 3m²)

2m⁴ - 2m - m

300

(6x² + 12x + 13x⁵) - (6x³ - 2x² - x⁵)

14x⁵ - 6x³ + 8x² + 12x

400

(11b⁴ - 10b⁵ + b²) - (8b⁴ - 11b² + 10b³)

-10b⁵ + 3b⁴ - 10b³ + 12b²

500

(13ab² - 6b²) - (-13b² - 8b³ + 8ab²) - (2b² + 13ab²)

-8ab² + 8b³ + 5b²

Multiplication

100

(4n - 2)(2n - 4)

8n² - 20n + 8

200

(5a - 4)(4a - 5)

20a² - 41a + 20

300

(-v - 5)(8v - 2)

-8v² - 38v + 10

400

(-8r - 5)(-7r + 7)

56r² - 21r - 35

500

(-4x² - x -7)(x² - 5x + 6) 

-4x⁴ + 19x³ - 26x² + 29x - 42

Division

100

(3n³ + 4n² + 45n)/9n

n²/3 + 4n/9 + 5

200

(2x³ + 20x² + 5x)/10x²

x/5 + 2 + 1/2x

300

(8v³ - 31v² + 25v - 10)/(v - 3)

8v² - 7v + 4 + 2/(v - 3)

400

(x³ - 4x² - 38x + 41)/(x-8)

x² + 4x - 6 - 7/(x - 8)

500

(a³ + 4a² - 35a + 31)/(a - 8)

a² + 4a - 3 + 7/(a - 8)

Definitions

100

the number which comes before a variable

coefficient

200

a mathematical expression with multiple terms which can't be reduced

a polynomial

300

simplifying an expression so each variable order only appears once

collecting like terms

400

the part that goes on the outside of the long division sign.

the divisor

500

the expressions that can be multiplied together to get a third expression

the factors.