Factoring Polynomials

GCF

100

50x + 100 

50(x + 2) 

200

63m³ - 21m² + 49m 

7m(9m² - 3m + 7) 

300

4x²y + 2x 

2x (2xy + 1) 

400

32m⁴n² - 56mn³ + 72n²

8n² (4m⁴ - 7mn + 9)

500

10a⁵b³ - 32a³b² + 16a²b⁴ - 6ab⁶

2ab² ( 5a⁴b - 16a + 8ab² - 3b⁴) 

Difference of Squares

100

x² - 25

(x - 5)(x + 5)

200

9m² - 16

(3x - 4)(3x + 4) 

300

36x² - 49y²

(6x - 7y)(6x + 7y)

400

20x² - 5

5(2x - 1)(2x + 1) 

500

2x⁴ - 162

2(x² + 9)(x - 3)(x + 3) 

Sum & Difference of Cubes

100

x³ + 8

(x + 2)(x² - 2x + 4)

200

27m³ - 125

(3m - 5)(9m² + 15m + 25)

300

54y³ + 1024

2(3y + 8)(9y² - 24y + 64)

400

108 - 4n³

4(3 - n)(9 + 3n + n²)

500

81a³ - 192b³

3(3a - 4b)(9a² + 12ab + 16b²)

Trinomials

100

x² - 10x + 9

(x - 1)(x - 9) 

200

3m² + 33a + 54

3(a + 2)(a + 9) 

300

3p² - 2p - 5

(3p - 5)(p + 1) 

400

3n³ - 8n² + 4n

n(n - 2)(3n - 2)

500

12m⁴ - 11m² + 2

(3m² - 2)(2m + 1)(2m - 1) 

Grouping

100

12a³ - 9a² + 4a - 3

(3a² + 1)(4a - 3)

200

35xy - 5x - 56y + 8

(5x - 8)(7y - 1) 

300

105ab - 90a - 21b + 18

3(5a - 1)(7b - 6)

400

192x²y + 72x³ - 24rxy - 9rx²

3x(8x - r)(8y + 3x)

500

12p³ + 20p² - 48p - 80

4(p + 2)(p - 2)(3p + 5)