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Example: Find the GCF of 4 and 18 4 = 1 * 2 * 2 18 = 1 * 2 * 3 * 3 So, the GCF is 2.

GCF means Greatest Common Factor. Example: Find the GCF of 4 and 18 4 = 1 * 2 * 2 18 = 1 * 2 * 3 * 3 So, the GCF is 2. Find the GCF: 42 and 56 48 and 84 9, 15, and 24. What’s the GCF of 5x 2 and 10x?. List the prime factorization of each monomial:.

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Example: Find the GCF of 4 and 18 4 = 1 * 2 * 2 18 = 1 * 2 * 3 * 3 So, the GCF is 2.

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  1. GCF means Greatest Common Factor Example: Find the GCF of 4 and 18 4 = 1 * 2 * 2 18 = 1 * 2 * 3 * 3 So, the GCF is 2.

  2. Find the GCF: • 42 and 56 • 48 and 84 • 9, 15, and 24

  3. What’s the GCF of 5x2 and 10x? List the prime factorization of each monomial: Find the greatest factor they have in common:

  4. We can use GCF to help us factor polynomials. To factor a polynomial means: to express it as the product of monomials and polynomials

  5. So, to factor a polynomial using the GCF: • Find the GCF of the terms. • Factor out this GCF and decide what is left inside the parentheses. (Divide each term by the GCF.) • Example: Factor 5x2 + 10x

  6. Factor:

  7. Zero Product Property If the product of two factors is 0, then at least one of the factors must be 0.

  8. Example: Solve (d – 5)(3d + 4) = 0. If (d – 5)(3d + 4) = 0, then according to the Zero Product Property either d – 5 = 0 or 3d + 4 = 0. (d – 5)(3d + 4) = 0 original equation d – 5 = 0 or 3d + 4 = 0 set each factor = 0 d = 5 3d = - 4 solve each equation d = - 4/3 The solution set is {5, - 4/3}.

  9. Example: Solve 3x2 + 9x = 0. Check the solutions.

  10. Exit Pass: • Find the GCF of 12 and 20 • Find the GCF of 34x2y and 17xy2 • Factor using the GCF: 12c5 + 6c3 – 3c2

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