PolyPardy

Addition and Subtraction of polynomials

100

(2x² – x⁴ + 5) + (7x² + 2x⁴ – 10)

 = 9x² + x⁴ – 5

200

(4y² – 9y + 8) - (3y² – 7y + 13)

= y² – 2y – 5

300

(9k + 5k² – 13) + (6 + 4k³ – 14k)

= 4k³ + 5k² – 5k – 7

400

(4b⁵ + b⁴ + 3b³ – 3b + 5) + (3b⁵ + 4b³ + 8b + 3)

= 7b⁵ + b⁴ + 7b³ + 5b + 8

500

(2r – 5r³ + 2r⁵ – 9) – (-10r⁵ + 2r⁴ – 5r + 6 + 2a³)

= 7r – 5r³ + 12r⁵ – 15 – 2r⁴ – 2a³

Multiplication and Division of polynomials

100

(n – 5)(n + 10)

= n² + 5n – 50

200

51u³v – 57u²v + 15 / 3uv

= 17u² – 19uv + 5uv

300

(5 + d)(3d + 2 – d²)

= -d³ – 2d² + 17d + 10

400

y³ – 3y² – 2y – 5 / y + 2

= y² + 5y – 12 + (19/y + 2)

500

(x² + 3x + 1)(x² – x – 2)

= x⁴ + 2x³ – 4x² – 7x – 2

Factors of perfect square trinomial

100

x² + 10x + 25

= (x + 5)²

200

r² - 8r + 16

= (r - 4)²

300

15x² - 16x - 7

= (3x + 1)(5x - 7)

400

81x² - 36xy + 4y²

(9x - 2y)²

500

(7x + 9y)²

= 49x2 + 126xy + 81y²

Factors of quadratic trinomials

100

a² + ya + 1

= (a + y)(a-1)

200

x² – 8x + 15

= (x – 5)(x – 3)

300

q² + 7q + 10

= (q + 5)(q + 2)

400

3x² – 19x + 28

= (3x – 7)(x – 4)

500

r² + 15r + 26

= (r + 13)(r + 2)

Common monomial factoring

100

14x⁶ + 56x³

= 14x³(x³ + 4)

200

54x²y³ + 36x⁴y²z

= 9x³y²(6y + 4x²)

300

9cm + c + 9dm + d

= (9m + 1)(c + d)

400

28x²y – 56y + 77k²

= 7y(4x² – 8 + 11k²)

500

42c³f – 126c⁵ – 21c⁴

 = 21c³(2f – 6c² – c)