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Mastering Factoring: Finding the Greatest Common Factor (GCF)

Learn how to find the GCF of terms and polynomials, the largest factor that divides them evenly. Follow steps, examples, and practice to enhance your factoring skills efficiently.

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Mastering Factoring: Finding the Greatest Common Factor (GCF)

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  1. Topic: FactoringMI: Finding GCF(Greatest Common Factor) Do Now: Multiply 5a.6a² 2a(3a + 2b)

  2. Factors: Terms multiplied together to form a product. (5a)(6a²) = 30a³ Greatest Common Factor: Largest factors of two or more terms. Greatest number or variable that can go into all terms 8, 24 GCF= 2a, 3a² GCF= 24a³b, 8ab² GCF=

  3. Steps to finding GCF for two monomials • Find greatest number that can go into all coefficients. • For each variable find smallest exponent that can go into both terms (highest variable). 9st, 12tg GCF= 56m²n², 8m²n GCF=

  4. 1. 2a + 2b Steps Find GCF for each term of polynomial. Divide each term by GCF. Answer is shown as product of GCF and remainder terms. Check by multiplication. Factoring Polynomials for GCF

  5. Examples • 3x – 3y • bx + by • 15c – 10d • 2x³ - 3x² + 5x

  6. Now you try!!!! • 6x + 3 • 2x² + 8x e) 10x²y – 15xy² • 24x² - 8x d) 10x² + 35x f) 12x² -9x + 15

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  8. Negative Coefficients

  9. Summary • Summary • How do we factor 
a polynomial with a 
GCF?

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