Factoring!

GCF

100

 5z^2+45z 

5z(z+9)

200

 6d^3-21d^2 

3d^2(2d-7)

300

  5n^6+2n^5 

n^5(5n+2)

400

 3x^2y-6xy^2+15xy 

3xy(x-2y+5)

500

5a^3b^2c^2-5a^2b^3c^2+5a^2b^2c^3

5a^2b^2c^2(a-b+c)

a=1

100

 x^2+5x+6 

(x+2)(x+3)

200

 y^2-8y+12 

(y-2)(y-6)

300

 n^2+16n+64 

(n+8)(n+8)

400

 -7m+m^2-30 

(m+3)(m-10)

500

 p^2+31p+84 

(p+3)(p+28)

a not =1

100

 3h^2+5h-2 

(h+2)(3h-1)

200

 6x^2-5x+1 

(2x-1)(3x-1)

300

 4k^2-12k+9 

(2k-3)(2k-3)

400

 14x^2+3x-2  

(2x+1)(7x-2)

500

 8m^2+30m+7   

(4m+1)(2m+7)

Special Product (i.e., difference of squares)

100

 x^2-4 

(x+2)(x-2)

200

 z^2-121  

(z+11)(z-11)

300

 64-16d^2  

(8+4d)(8-4d)

400

 4a^2-49b^2

(2a+7b)(2a-7b)

500

 25m^2-81n^2 

(5m+9n)(5m-9n)

Grouping

100

 x^3+x^2+2x+2 

(x+1)(x^2+2)

200

  x^2+xy+8x+8y

(x+y)(x+8)

300

 3z^3+2z-12z^2-8 

(3z^2+2)(z-4)

400

 m^2-3m+mn-3n 

(m-3)(m+n)

500

 2a^2+8ab-3a-12b 

(a+4b)(2a-3)

General

100

 5x^2+15x+10 

5(x+1)(x+2)

200

 36a^4-4a^2 

4a^2(3a+1)(3a-1)

300

 x^2-5x-35 

Not factorable :(

400

   8b^3-4b^2a-18b+9a  

(2b-a)(2b+3)(2b-3)

500

x^4-y^4

(x^2+y^2)(x+y)(x-y)