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Factoring Using the Distributive Property

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.

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Factoring Using the Distributive Property

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  1. Factoring Using the Distributive Property Chapter 9.2

  2. Factoring using Distribution • Remember the distributive property: 2x(3x + 2) 6x2 + 4x

  3. Factoring using Distribution • Today we are going to use the distributive property in reverse! • This is a different type of factoring

  4. 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 12x = 2 * 2 *3 * x 80 = 2 * 2 * 2 * 2 * 5

  5. Factoring using Distribution 12x = 2 * 2 *3 * x • Find the GCF 80 = 2 * 2 * 2 * 2 * 5 GCF = = 4 2 * 2

  6. 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 4 4 3x + 20

  7. 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

  8. Factoring using Distribution Practice • Factor the following: 1. 24x + 18 2. 60x + 210 4. 13x + 23 3. -25 – 40x 5. 18x + 72

  9. Factoring using Distribution Practice • Factor the following: 1. 24x + 18 2. 60x + 210 30(2x + 7) 6(4x + 3) 4. 13x + 23 3. -25 – 40x Not Factorable -5(5 – 8x) 5. 18x + 72 18(x + 4)

  10. Factoring using Distribution 6x2 – 9x • Example 2: Factor • Find the GCF 6x2 = 2 * 3 * x * x –9x = -1 * 3 * 3 * x 3x GCF =

  11. Factoring using Distribution • Take 3x out of the original problem • Check your answer 6x2 – 9x 2x 3x ( – 3)

  12. Factoring using Distribution Practice • Factor the following: 1. 24x2 + 15x 2. 80x4 + 200x2 4. 13x + 52x3 3. 21x – 39x3 5. 28x3y3 + 98x2y

  13. Factoring using Distribution Practice • Factor the following: 1. 24x2 + 15x 2. 80x4 + 200x2 40x2(2x2 + 5) 3x(8x + 5) 4. 13x + 52x3 3. 21x – 39x3 13x(1 + 4x2) 3x(7 – 13x2) 5. 28x3y3 + 98x2y 14x2y(2x y2+ 7)

  14. Factoring using Distribution 6x2 – 9x = 0 • Example 2: Factor • Find the GCF on the left side 6x2 = 2 * 3 * x * x –9x = -1 * 3 * 3 * x 3x GCF =

  15. Factoring using Distribution • Take 3x out of the original problem • Now we have to solve the problem 6x2 – 9x = 0 2x = 0 3x ( – 3)

  16. Factoring using Distribution • Remember, if x*y = 0 then either x or y has to be zero 2x = 0 3x ( – 3) • Therefore either 3x or (2x – 3) has to equal 0

  17. Factoring using Distribution • Set each one equal to zero and solve separately 3x = 0 2x = 0 – 3 x = 0 +3+3 = 3 2x 3 __ _ x = 2 2 2

  18. 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 = 0 3 x = 2

  19. Factoring using Distribution • Plug in x = 0 • This works! 6(0)2 – 9(0) = 0 6(0) – 9(0) = 0 0 – 0 = 0

  20. Factoring using Distribution 3 3 6( )2 – 9( ) = 0 • Plug in 3/2 for x • This works too! 2 2 9 3 6( ) – 9( ) = 0 4 2 27 27 – = 0 2 2 0 = 0

  21. Factoring using Distribution Practice • Factor the following: 1. 3x2 + 12x = 0 2. x2 = 7x 4. 52x2 + 13x3 = 0 3. 12x(x – 9) = 0 5. 9x2 = 27x

  22. Factoring using Distribution Practice • Factor the following: 1. 3x2 + 12x = 0 2. x2 = 7x 0 and 7 0 and -4 4. 52x2 + 13x3 = 0 3. 12x(x – 9) = 0 0 and -4 0 and 9 5. 9x2 = 27x 0 and 3

  23. Factoring using Distribution • Example 3: Factor the following • Once again, find the GCF of all three numbers 2x5 + 6x3 – 8x2 GCF = 2x2

  24. Factoring using Distribution 2x5 + 6x3 – 8x2 • Take 2x2 out of the original equation + 3x x3 – 4) 2x2 (

  25. Factoring using Distribution Practice • Factor each equation 1. 6x3 + 15x2 – 9x 2. 12x4 + 48x3 + 36x2 4. 16x3 + 32x2 + 24x 3. 18x + 36x2 – 81x3 5. 70x3y3 + 105x2y – 175xy2

  26. Factoring using Distribution Practice • Factor each equation 1. 6x3 + 15x2 – 9x 2. 12x4 + 48x3 + 36x2 12x2(x2 + 4x + 3) 3x(2x2 + 5x – 3) 4. 16x3 + 32x2 + 24x 3. 18x + 36x2 – 81x3 8x(2x2 + 4x + 3) 9x(2 + 4x – 9x2) 5. 70x3y3 + 105x2y – 175xy2 35xy(2x2 y2+ 3x – 5y)

  27. Factoring using Distribution Quiz • Factor the following 1. -9x – 3 2. 12x4 + 18x3 4. 16x2 – 80x = 0 3. 24x2y3 – 84xy2 5. 45x3 + 63x2 + 9x

  28. Factoring using Distribution Quiz • Factor the following 1. -9x – 3 2. 12x4 + 18x3 6x3(2x + 3) -3(3x + 1) 4. 16x2 – 80x = 0 3. 24x2y3 – 84xy2 0 and 5 12xy2(2xy – 7) 5. 45x3 + 63x2 + 9x 9x(5x2 + 7x + 1)

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