Factoring Using the Distributive Property
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Transcript of 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
Factoring using Distribution•Factor the following:
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)
Factoring using Distribution•Factor the following:
1. 24x2 + 15x
4. 13x + 52x33. 21x – 39x3
2. 80x4 + 200x2
5. 28x3y3 + 98x2y
Practice
Factoring using Distribution•Factor the following:
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
Factoring using Distribution•Factor the following:
1. 3x2 + 12x = 0
4. 52x2 + 13x3 = 0
3. 12x(x – 9) = 0
5. 9x2 = 27x
2. x2 = 7x
Practice
Factoring using Distribution•Factor the following:
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)