Algebra

Greatest common factor

100

5(x+5)

what is 5x+25

200

2(x-8)

what is 2x-16

300

45, 60, 30 

15

400

12, 48, 24

12

500

42, 28, 56 

14

factoring trinomials

100

x^2+7x+6

(x+6)x(x+1)

200

x^2-7x-8

(x+1)x(x-8)

300

x^2-6x-27

(x+3)x(x-9)

400

x^2+4xy-12y^2

(x+6y)x(x-2y)

500

p^2+14p+40

(p+4)(p+10)

difference of perfect square

100

x^2-64

(x-8)x(x+8)

200

1-x^2

(1-x)x(1+x)

300

49x^2-144

(7x-12)x(7x+12)

400

121x^2-81

(11x-9)x(11x+9)

500

150k^2-216

6(5k+6)(5k-6)

factoring by grouping

100

4au+24av-5bu-30bv

(4a-5b)(u+6v)

200

12a^2+36a-3a-9

3[(a+3)(4a-1)]

300

42ab-25ab-35a+30b^2

(7a+5b)(6b-5)

400

15xy-12vx-12x^2+15vy 

3(x+v)(5y-4x)

500

125m^2n-30mp-50m^2+75mpn

5m(5m+3p)(5n-2)

polynomial functions

100

f(x)=x^5-7x^4+10x^3+14x^2-24x

f'(x)=5x^4-28x^3+30x^2+28x-24

200

f(x)=x^4-13x^2-12x

f'(x)=4x^3-26x-12

300

f(x)=x^4-7x^2+12

f'(x)=4x^3-14x

400

f(x)=x^3-6x^2+11x-6

f'(x)=3x^2-12x+11

500

f(x)=x^3-9x^2+20x-12

f'(x)=3x^2-18x+20