Algebra I - Chapter 7

Factor by GCF

100

8x^4-12x^2

4x²(2x²-3)

200

3v^2-27v-33

3v^2-27v-33

3(v^2-9v-11)

300

16m^2-2m^3+32m

16m^2-2m^3+32m

-2m(m^2-8m-16)

400

8ax^4+28ax^3+56ax^2+16ax

8ax^4+28ax^3+56ax^2+16ax

4ax(x^3+7x^2+14x+4)

500

48a^2b^4c - 32ab^6c^5+80a^2b^4c^3

48a^2b^4c - 32ab^6c^5+80a^2b^4c^3

16ab^4c(3a-2b^2c^4+5ac^2)

Factoring Trinomials

100

x^2 + 8x +12

(x+6)(x+2)

200

m^2-11m+18

(m-9)(m-2)

300

x^2+5x-24

(x+8)(x-3)

400

y^2-2y-48

(y-8)(y+6)

500

x^2-x-56

(x-8)(x+7)

Factoring Trinomials - AC Method

100

2x^2+7x+3

2x^2+7x+3

2x^2+6x+x+3

2x(x+3)+1(x+3)

(2x+1)(x+3)

200

5n^2+26n+5

5n^2+26n+5

5n^2+1n+25n+5

n(5n+1)+5(5n+1)

(n+5)(5n+1)

300

3x^2-10x+7

3x^2-10x+7

3x2-3x-7x+7

3x(x-1)-7(x-1)

(3x-7)(x-1)

400

7x^2-36x+5

7x^2-36x+5

7x^2-35x-x+5

7x(x-5)-1(x-5)

(7x-1)(x-5)

500

2x^2-12x+10

2x^2-12x+10

2(x^2-6x+5)

2(x-5)(x-1)

Factor by Grouping

100

12p^3-21p^2+28p-49

12p^3-21p^2+28p-49

3p^2(4p-7)+7(4p-7)

(3p^2+7)(4p-7)

200

6v^3-16v^2+21v-56

2v^2(3v-8)+7(3v-8)

(2v^2+7)(3v-8)

300

8r^3-64r^2+r-8

8r^3-64r^2+r-8

8r^2(r-8)+1(r-8)

(8r^2+1)(r-8)

400

12x^3+2x^2-30x-5

12x^3+2x^2-30x-5

2x^2(6x+1)-5(6x+1)

(2x^2-5)(6x+1)

500

25v^3+5v^2-5v-1

25v^3+5v^2-5v-1

5v^2(5v+1)-1(5v+1)

(5v^2-1)(5v+1)

Difference of Perfect Squares

100

g^2 - 36

(g-6)(g+6)

200

9y^6-16

(3y^3-4)(3y^3+4)

300

-81 + c^10

-81 + c^10

c^10 - 81

(c^5-9)(c^5+9)

400

100r^2-9a^2

(10r+3a)(10r-3a)

500

49a^2b^4-1

(7ab^2+1)(7ab^2-1)

Next Level

100

x^3+15x^2+44x

x^3+15x^2+44x

x(x^2+15x+44)

x(x+11)(x+4)

200

5a^2-45

5(a^2-9)

5(a-3)(a+3)

300

8x^5-28x^4+4x^3-14x^2

2x^2(4x^3-14x^2+2x-7)

2x^2[2x^2(2x-7)+1(2x-7)]

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

400

32x^5-2x

2x(16x^4-1)

2x(4x^2+1)(4x^2-1)

2x(4x^2+1)(2x-1)(2x+1)

500

5b^3k^2+25b^2k^2-45bk^2-225k^2

5b^3k^2+25b^2k^2-45bk^2-225k^2

5k^2(b^3+5b^2-9b-45)

5k^2[b^2(b+5)-9(b+5)]

5k^2(b^2-9)(b+5)

5k^2(b+3)(b-3)(b+5)