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Lesson 10.4B : Factoring out GCMF

Lesson 10.4B : Factoring out GCMF Factor Completely – to express as the product of prime factors Ex. Factor completely : 24. 6 4. 2  2  2  3. 2 3. 2 2. Factor the following completely: 1) 5x 2 2) 14x 2 y 3. GCF = 6. GCF of 12 and 18.

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Lesson 10.4B : Factoring out GCMF

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  1. Lesson 10.4B : Factoring out GCMF Factor Completely – to express as the product of prime factors Ex. Factor completely : 24 6 4 2  2  2  3 2 3 2 2 Factor the following completely: 1) 5x2 2) 14x2y3

  2. GCF = 6 GCF of 12 and 18 GCF of 12x4y3 and 18xy5 GCF = 6xy3 GCMF : Greatest Common Monomial Factor – The greatest monomial that is a factor (will divide EVENLY into) of all the given monomials.

  3. To find the GCMF of two or more Monomials • First find the GCF of the coefficients • Find the largest power of each variable that is COMMON to all the monomials • The GCMF = product of GCF of coefficients and common variable factors

  4. Ex. Find GCMF of 12x2 and 18x GCF of coefficients = 6 Common variable(s) : only have one x in common GCMF = 6x Find GCMF of 21x2 and 35x5 GCF of Coefficients = 7 Common variable factors : two x’s GCMF = 7x2

  5. Find GCMF of 24x2y3 and 36x3y GCF of coefficients = 12 Common variable factors : two x’s and one y GCMF = 12x2y NOW, we are going to use GCMF’s to Factor Quadratic Expressions. Factoring Out the GCMF is the inverse (un-doing) of the Distributive Property

  6. To factor – undoing distributive property 1) Perform Distributive Property: 6(2 + 3) 12 + 18 Factor : 12 + 18 6 (2 + 3) 2) Use Distributive Property to simplify: 3(x + 7) 3x + 21 Factor: 3x + 21 3(x + 7) 3) Factor: 12x2y – 14xy3 2xy(6x – 7y2)

  7. Ex.Distribute 3x(x + 5) Means to multiply the 3x through the (x + 5) 3x(x) + 3x(5) 3x2 + 15x Ex. Factor 3x2 + 15x Means to Divide the GCMF out of the polynomial (divide each term by GCMF) GCMF = 3x Recall how to divide by monomial Divide (3x2 + 15x) by GCMF (3x) Factored form is 3x(x + 5)

  8. To factor a polynomial by factoring out the GCMF: • Find the GCMF • Divide the polynomial (each term of the polynomial) by the GCMF • Write the polynomial as the product of the GCMF and the result from step #2

  9. Example: Factor • 15x2 – 9 • Step 1) GCMF = 3 • Step 2) Divide 15x2 – 9 by the GCMF Step 3) Write as a product of GCMF and result of step 2 3(5x2 – 3)

  10. Factor • 28a3-12a2 • GCMF = 4a2 2) 15a – 25b + 20 GCMF = 5 Factored Form 5(3a-5b+4) Factored Form 4a2(7a – 3) 3) 16x5 – 14x3 + 26x2 GCMF = 2x2 Factored Form 2x2(8x3 – 7x + 13)

  11. Homework : Worksheet

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