Download - Factoring Using the Distributive Property

Factoring Using the Distributive PropertyChapter 9.2

Factoring using Distribution•Remember the distributive property:

2x(3x + 2)6x2 + 4x

Factoring using Distribution•Today we are going to use the distributive

property in reverse!

•This is a different type of factoring

Factoring using Distribution•Example 1: Use the distributive property

to factor:

•In order to factor this, we need to find the GCF (greatest common factor)

•Factor each number

12x + 80

80 = 2 * 2 * 2 * 2 * 512x = 2 * 2 *3 * x

Factoring using Distribution

•Find the GCF

12x = 2 * 2 *3 * x80 = 2 * 2 * 2 * 2 * 5GCF =2* 2 = 4

Factoring using Distribution•We are now going to

take the GCF out of each number

•We can divide each number by 4

•Now we have a different equation, so to keep it the same we have to keep the 4 with it

12x + 80___ __4 43x + 204

Factoring using Distribution•If we distributed the

4 we would end up with the same equation we started with

•So our answer is

4(3x + 20)12x + 80

Factoring using Distribution•Factor the following:

1. 24x + 18

4. 13x + 23

3. -25 – 40x

5. 18x + 72

2. 60x + 210

Practice


1. 24x + 18

4. 13x + 23

3. -25 – 40x

5. 18x + 72

2. 60x + 2106(4x + 3)

-5(5 – 8x)

18(x + 4)

Not Factorable

30(2x + 7)

Practice

Factoring using Distribution•Example 2: Factor

•Find the GCF

6x2 – 9x

–9x = -1 * 3 * 3 * x6x2 = 2 * 3 * x * x

GCF =3x

Factoring using Distribution•Take 3x out of

the original problem

•Check your answer

6x2 – 9x3x(2x – 3)


1. 24x2 + 15x

4. 13x + 52x33. 21x – 39x3

2. 80x4 + 200x2

5. 28x3y3 + 98x2y

Practice


1. 24x2 + 15x

4. 13x + 52x33. 21x – 39x3

5. 28x3y3 + 98x2y

2. 80x4 + 200x2

3x(8x + 5)

3x(7 – 13x2)

14x2y(2x y2+ 7)

40x2(2x2 + 5)

13x(1 + 4x2)

Practice

Factoring using Distribution•Example 2: Factor

•Find the GCF on the left side

6x2 – 9x = 0

–9x = -1 * 3 * 3 * x6x2 = 2 * 3 * x * x

GCF =3x

Factoring using Distribution•Take 3x out of

the original problem

•Now we have to solve the problem

6x2 – 9x = 03x(2x – 3)= 0

Factoring using Distribution•Remember, if x*y = 0 then either x or y

has to be zero 3x(2x – 3)= 0•Therefore either 3x or (2x – 3) has to equal 0

Factoring using Distribution•Set each one equal to zero and solve

separately3x 2x – 3 = 0= 0x= 0 +3 +3

2x= 3__ _ 2 2x = 3

2

Factoring using Distribution•So for these problems,

there can be 2 answers for x

•If you plug in either one, the equation should equal zero

x= 0x = 3

2

Factoring using Distribution•Plug in x = 0

•This works!

6(0)2 – 9(0) = 06(0) – 9(0) = 0

0 – 0 = 0

Factoring using Distribution•Plug in 3/2 for x

•This works too!

6( )2 – 9( ) = 032

3232

946( ) – 9( ) = 0272

272– = 00 = 0


1. 3x2 + 12x = 0

4. 52x2 + 13x3 = 0

3. 12x(x – 9) = 0

5. 9x2 = 27x

2. x2 = 7x

Practice


1. 3x2 + 12x = 0

4. 52x2 + 13x3 = 0

3. 12x(x – 9) = 0

5. 9x2 = 27x

2. x2 = 7x0 and -4

0 and 9

0 and 3

0 and 7

0 and -4

Practice

Factoring using Distribution•Example 3: Factor the following

•Once again, find the GCF of all three numbers

2x5 + 6x3 – 8x2

GCF = 2x2

Factoring using Distribution

•Take 2x2 out of the original equation

2x5 + 6x3 – 8x2

2x2( + 3xx3 – 4)

Factoring using Distribution•Factor each equation

1. 6x3 + 15x2 – 9x

4. 16x3 + 32x2 + 24x

3. 18x + 36x2 – 81x3

5. 70x3y3 + 105x2y – 175xy2

2. 12x4 + 48x3 + 36x2

Practice

Factoring using Distribution•Factor each equation

1. 6x3 + 15x2 – 9x

4. 16x3 + 32x2 + 24x

3. 18x + 36x2 – 81x3

5. 70x3y3 + 105x2y – 175xy2

2. 12x4 + 48x3 + 36x23x(2x2 + 5x – 3)

9x(2 + 4x – 9x2)

35xy(2x2 y2+ 3x – 5y)

12x2(x2 + 4x + 3)

8x(2x2 + 4x + 3)

Practice

Factoring using Distribution•Factor the following

1. -9x – 3

4. 16x2 – 80x = 03. 24x2y3 – 84xy2

2. 12x4 + 18x3

Quiz

5. 45x3 + 63x2 + 9x

Factoring using Distribution•Factor the following

1. -9x – 3

4. 16x2 – 80x = 03. 24x2y3 – 84xy2

2. 12x4 + 18x3

-3(3x + 1)

12xy2(2xy – 7)

6x3(2x + 3)

0 and 5

Quiz

5. 45x3 + 63x2 + 9x 9x(5x2 + 7x +

1)

Download - Factoring Using the Distributive Property

Top Related