Alg1 - 7.5-7.9: Factoring Polynomials

7.6 Factor GCF

100

Factor 

14a-7

7(2a-1)

200

Factor

18x^2y^2-30x

6x(3xy^2-5)

300

Factor 

a^3b^3-2b^2

b^2(a^3b-2)

400

Factor

10m^5n^2 + 25m^3n^3

5m^3n^2(2m^2+5n)

500

Factor 

4p^3-18p^2q^2+2p

2p(2p^2-9pq^2+1)

600

Factor 

45c^8-72c^5-27c^2

9c^2(5c^6-8c^3-3)

7.7 Factor when a=1

100

Factor 

x^2+8x+12

(x+6)(x+2)

200

Factor 

k^2-16k+28

(k-14)(k-2)

300

Factor 

h^2+2h-35

(h+7)(h-5)

400

Factor 

c^2+7c-30

c^2+7c-30

(c+10)(c-3)

500

Factor 

h^2-12h-108

(h-18)(h+6)

600

Factor 

3r^3-9r^2-84r

3r(r^2-3r-28)

3r(r-7)(r+4)

7.8 Factor when a≠1

100

Factor 

3x^2+7x+2

(3x+1)(x+2)

200

Factor 

2n^2-11n+15

(2n-5)(n-3)

300

Factor 

4r^2+17r+15

(4r+5)(r+3)

400

Factor 

6k^2-19k-7

(3k+1)(2k-7)

500

Factor 

6g^2-39g+18

3(2g^2-13g+6)

3(2g-1)(g-6)

600

Factor

4a^2+6a-40

2(2a^2+3a-20)

2(2a-5)(a+4)

7.9 Special Products

100

Factor 

x^2-16

(x+4)(x-4)

200

Factor 

b^2-81

(b+9)(b-9)

300

Factor 

4a^2-25b^2

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

400

Factor 

27m^2-3

3(9m^2-1)

3(3m+1)(3m-1)

500

Factor 

4a^3-400a

4a(a^2-100)

4a(a-10)(a+10)

600

Factor 

80q^4r^2-5r^2

5r^2(16q^4-1)

5r^2(4q^2+1)(4q^2-1)

5r^2(4q^2+1)(2q+1)(2q-1)

Solving Polynomials

100

Solve 

x^2+14x+49=0

(x+7)(x+7)=0

x=-7

200

Solve. 

x^2+x-30=0

(x+6)(x-5)=0

x=-6, x=5

300

Solve 

2m^2+12m-32=0

2(m^2+6m-16)=0

2(m+8)(m-2)=0

m=-8, m=2

400

Solve 

x^3-13x^2+42x=0

x(x^2-13x+42)=0

x(x-6)(x-7)=0

x=0, x=6, x=7

500

Solve. 

10x^2-x-3=0

(5x-3)(2x+1)=0

x=3/5, x=-1/2

600

Solve 

6k^2-5k-4=0

(3k-4)(2k+1)=0

k=4/3, k=-1/2