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GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5 , A1.1.1.5.2

GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5 , A1.1.1.5.2. How can we use a greatest common factor of two or more monomials to solve problems ? How can we use a least common multiple of two or more monomials to solve problems ?

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GCF and LCM Section 2.3 Standards Addressed: A1.1.1.5 , A1.1.1.5.2

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  1. GCF and LCMSection 2.3Standards Addressed: A1.1.1.5, A1.1.1.5.2

  2. How can we use a greatest common factor of two or more monomials to solve problems? • How can we use a least common multiple of two or more monomials to solve problems? • When do we need to use a greatest common factor to model a situation? • When do we need to use a least common multiple to model a situation? Essential Questions

  3. You can find the Greatest Common Factor (GCF) of two or more monomials by finding the product of their common prime factors.

  4. Find the GCF of 16xy2 and 30xy3 Example 1

  5. Find the GCF of 16xy2 and 30xy3 16xy2: 2  2  2  2 x y y 30xy3: 2 3  5 xyy y Example 1

  6. Find the GCF of 16xy2 and 30xy3 16xy2: 2  2  2  2 x y y 30xy3: 2 3  5 xyy y Example 1

  7. Find the GCF of 16xy2 and 30xy3 16xy2: 2  2  2  2 x y y 30xy3: 2 3  5 xyy y Example 1 The GCF of 16xy2 and 30xy3 is 2xy2

  8. You can find the Least Common Multiple (LCM) of two or more monomials by multiplying the factors, using the common factors only once.

  9. Find the LCM of 18xy2 and 10y Example 2

  10. Find the LCM of 18xy2 and 10y 18xy2: 2  3  3 x y y 10y: 2  5y Example 2

  11. Find the LCM of 18xy2 and 10y 18xy2: 2  3  3 x y y 10y: 2  5y Example 2

  12. Find the LCM of 18xy2 and 10y 18xy2: 2  3  3 x y y 10y: 2  5y LCM: 2  3  3  5 x y y Example 2

  13. Find the LCM of 18xy2 and 10y 18xy2: 2  3  3 x y y 10y: 2  5y LCM: 2  3  3  5 x y y Example 2 The LCM of 18xy2 and 10y is 90xy2

  14. To factor a polynomial means to write the polynomial as a product of other polynomials. First, find the GCF of its terms (if the GCF exists). Next, use the distributive property to write the polynomial in factored form.

  15. Polynomial: 21x2 – 28xy3

  16. Polynomial: 21x2 – 28xy3Find the GCFof terms: 7x(3x) – 7x(4y3)

  17. Polynomial: 21x2 – 28xy3Find the GCFof terms: 7x(3x) – 7x(4y3)Use theDistributiveProperty: 7x(3x – 4y3)

  18. (A) 3x3y – 15x2y4 Example 3: Factor

  19. (B) 8m4n2 + 18m3n2 – 6m2n Example 3: Factor

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