factoring using the distributive property

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Factoring Using the Distributive Property. Chapter 9.2. Factoring using Distribution. Remember the distributive property:. 2x(3x + 2). 6x 2 + 4x. Factoring using Distribution. Today we are going to use the distributive property in reverse! This is a different type of factoring. - PowerPoint PPT Presentation

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Factoring Using the Distributive Property

Factoring Using the Distributive PropertyChapter 9.2Factoring using DistributionRemember the distributive property:2x(3x + 2)6x2 + 4xFactoring using DistributionToday we are going to use the distributive property in reverse!

This is a different type of factoringFactoring using DistributionExample 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 + 8080 = 2 * 2 * 2 * 2 * 512x = 2 * 2 *3 * xFactoring using DistributionFind the GCF12x = 2 * 2 *3 * x80 = 2 * 2 * 2 * 2 * 5GCF =2* 2= 4Factoring using DistributionWe are now going to take the GCF out of each numberWe can divide each number by 4Now we have a different equation, so to keep it the same we have to keep the 4 with it12x + 80___ __4 43x + 204Factoring using DistributionIf we distributed the 4 we would end up with the same equation we started withSo our answer is4(3x + 20)12x + 80Factoring using DistributionFactor the following:1. 24x + 184. 13x + 233. -25 40x5. 18x + 722. 60x + 210PracticeFactoring using DistributionFactor the following:1. 24x + 184. 13x + 233. -25 40x5. 18x + 722. 60x + 2106(4x + 3)-5(5 8x)18(x + 4)Not Factorable30(2x + 7)PracticeFactoring using DistributionExample 2: Factor

Find the GCF6x2 9x9x = -1 * 3 * 3 * x6x2 = 2 * 3 * x * xGCF =3xFactoring using DistributionTake 3x out of the original problem

Check your answer6x2 9x3x(2x 3)Factoring using DistributionFactor the following:1. 24x2 + 15x4. 13x + 52x33. 21x 39x32. 80x4 + 200x25. 28x3y3 + 98x2yPracticeFactoring using DistributionFactor the following:1. 24x2 + 15x4. 13x + 52x33. 21x 39x35. 28x3y3 + 98x2y2. 80x4 + 200x23x(8x + 5)3x(7 13x2)14x2y(2x y2+ 7)40x2(2x2 + 5)13x(1 + 4x2)PracticeFactoring using DistributionExample 2: Factor

Find the GCF on the left side6x2 9x = 09x = -1 * 3 * 3 * x6x2 = 2 * 3 * x * xGCF =3xFactoring using DistributionTake 3x out of the original problem

Now we have to solve the problem

6x2 9x = 03x(2x 3)= 0Factoring using DistributionRemember, if x*y = 0 then either x or y has to be zero3x(2x 3)= 0Therefore either 3x or (2x 3) has to equal 0

Factoring using DistributionSet each one equal to zero and solve separately3x2x 3= 0= 0x= 0+3 +32x= 3__ _ 2 2x =32Factoring using DistributionSo for these problems, there can be 2 answers for xIf you plug in either one, the equation should equal zerox= 0x =32Factoring using DistributionPlug in x = 0

This works!6(0)2 9(0) = 06(0) 9(0) = 00 0 = 0Factoring using DistributionPlug in 3/2 for x

This works too!6( )2 9( ) = 0323232946( ) 9( ) = 0272272 = 00 = 0Factoring using DistributionFactor the following:1. 3x2 + 12x = 04. 52x2 + 13x3 = 03. 12x(x 9) = 05. 9x2 = 27x2. x2 = 7xPracticeFactoring using DistributionFactor the following:1. 3x2 + 12x = 04. 52x2 + 13x3 = 03. 12x(x 9) = 05. 9x2 = 27x2. x2 = 7x0 and -40 and 90 and 30 and 70 and -4PracticeFactoring using DistributionExample 3: Factor the following

Once again, find the GCF of all three numbers

2x5 + 6x3 8x2GCF = 2x2Factoring using DistributionTake 2x2 out of the original equation

2x5 + 6x3 8x22x2(+ 3xx3 4)Factoring using DistributionFactor each equation1. 6x3 + 15x2 9x 4. 16x3 + 32x2 + 24x 3. 18x + 36x2 81x35. 70x3y3 + 105x2y 175xy22. 12x4 + 48x3 + 36x2PracticeFactoring using DistributionFactor each equation1. 6x3 + 15x2 9x 4. 16x3 + 32x2 + 24x 3. 18x + 36x2 81x35. 70x3y3 + 105x2y 175xy22. 12x4 + 48x3 + 36x23x(2x2 + 5x 3)9x(2 + 4x 9x2)35xy(2x2 y2+ 3x 5y)12x2(x2 + 4x + 3)8x(2x2 + 4x + 3)PracticeFactoring using DistributionFactor the following1. -9x 3 4. 16x2 80x = 03. 24x2y3 84xy22. 12x4 + 18x3Quiz5. 45x3 + 63x2 + 9x Factoring using DistributionFactor the following1. -9x 3 4. 16x2 80x = 03. 24x2y3 84xy22. 12x4 + 18x3-3(3x + 1)12xy2(2xy 7)6x3(2x + 3)0 and 5Quiz5. 45x3 + 63x2 + 9x 9x(5x2 + 7x + 1)