FACTORING and SOLVING POLYNOMIALS

Factoring Trinomials, a=1

1

Factor into two binomials: 

x²-x-56

(x-8)(x+7)

2

Factor into two binomials: 

x²+8x+12

(x+6)(x+2)

3

Factor into two binomials: 

x²+5x-24

(x+8)(x-3)

4

Factor into two binomials: 

y²-6y-7

(y-7)(y+1)

5

Factor into two binomials: 

m²-11m+18

(m-9)(m-2)

Factoring Trinomials, a>1

1

Factor into two binomials: 

2x²-12x+10

2(x-1)(x-5)

2

Factor into two binomials: 

2x²+7x+3

(2x+1)(x+3)

3

Factor into two binomials: 

3x²-10x+7

(3x-7)(x-1)

4

Factor into two binomials: 

7x²-36x+5

(7x-1)(x-5)

5

Factor into two binomials: 

5n²+26n+5

(5n+1)(n+5)

Factor Monomials

1

Find the GCF: 

12m⁴n³, 6m³n², 24m²n⁴

6m²n²

2

Find the GCF: 

3x², 12x

3x

3

Find the GCF: 

2x⁵, 9x⁴

x⁴

4

Find the GCF: 

18x³, 32x²+6x

2x

5

Find the GCF: 

4x³, 10x²

2x²

Factor Binomials

1

Factor by GCF: 

10a³b⁴-6a²b⁶

2a²b⁴(5a-3b²)

2

Factor by GCF: 

14n²+10n

2n(7n+5)

3

Factor by GCF: 

8-4a²

4(2-a²)

4

Factor by GCF: 

4x⁴+16x³-8x²

4x²(x²+4x-2)

5

Factor by GCF: 

18x³-6x

6x(3x²-1)

Miscellaneous Solving

1

Solve by factoring

−4k² − 8k − 3 =  −3 − 5k²

x=8 x=0

2

Solve for x: 

3x-7=11

x=6

3

Solve for x:

5(2x + 6) = −4(−5 − 2x) + 3x

x=10

4

Solve by factoring:  

2x²+x-21=0

Factors to: (2x+7)(x-3)=0

Solutions are: x= -7/2 , x=3

5

Solve for x:

2x+8=5x-7

x=5