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Factoring Polynomials

Factoring Polynomials. Algebra I. Vocabulary. Factors – The numbers used to find a product. Prime Number – A whole number greater than one and its only factors are 1 and itself. Composite Number – A whole number greater than one that has more than 2 factors. Vocabulary.

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Factoring Polynomials

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  1. Factoring Polynomials Algebra I

  2. Vocabulary • Factors – The numbers used to find a product. • Prime Number – A whole number greater than one and its only factors are 1 and itself. • Composite Number – A whole number greater than one that has more than 2 factors.

  3. Vocabulary • Factored Form – A polynomial expressed as the product of prime numbers and variables. • Prime Factoring – Finding the prime factors of a term. • Greatest Common Factor (GCF) – The product of common prime factors.

  4. Prime or Composite? Ex) 36 Ex) 23

  5. Prime or Composite? Ex) 36 Composite. Factors: 1,2,3,4,6,9,12,18,36 Ex) 23 Prime. Factors: 1,23

  6. Prime Factorization Ex) 90 = 2 ∙ 45 = 2∙ 3∙ 15 = 2∙ 3 ∙ 3 ∙ 5 OR use a factor tree: 90 9 10 3 3 2 5

  7. Prime Factorization of Negative Integers Ex) -140 = -1 ∙ 140 = -1 ∙ 2 ∙ 70 = -1 ∙ 2 ∙ 7 ∙ 10 = -1 ∙ 2 ∙ 7 ∙ 2 ∙ 5

  8. Now you try… Ex) 96 Ex) -24

  9. Now you try… Ex) 96 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 Ex) -24 -1 ∙ 2 ∙ 2 ∙ 2 ∙ 3

  10. Prime Factorization of a Monomial 12a²b³= 2 · 2 · 3 · a · a · b · b · b -66pq²= -1 · 2 · 3 · 11 · p · q · q

  11. Finding GCF Ex) 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 60 = 2 ∙ 2 ∙ 3 ∙ 5 GCF = 2 · 2 · 3 = 12 Ex) 15 = 3 · 5 16 = 2 · 2 · 2 · 2 GCF – none = 1

  12. Now you try… Ex) 36x²y 54xy²z

  13. Now you try… Ex) 36x²y = 2 · 2 · 3 · 3 · x · x · y 54xy²z = 2 · 3 · 3 · 3 · x · y · y · z GCF = 18xy

  14. Factoring Using the (Reverse) Distributive Property • Factoring a polynomial means to find its completely factored form.

  15. Factoring Using the (Reverse) Distributive Property • First step is to find the prime factors of each term. Ex) 12a²+ 16a 12a²= 2 · 2 · 3 · a · a 16a = 2 · 2 · 2 · 2 · a

  16. Factoring Using the (Reverse) Distributive Property • First step is to find the prime factors of each term. • Next step is to find the GCF of the terms in the polynomial. Ex) 12a²+ 16a 12a²= 2 · 2 · 3 · a · a 16a = 2 · 2 · 2 · 2 · a GCF = 4a

  17. Factoring Using the (Reverse) Distributive Property • First step is to find the prime factors of each term. • Next step is to find the GCF of the terms in the polynomial. • Now write what is left of each term and leave in parenthesis. Ex) 12a²+ 16a 12a²= 2 · 2 · 3 · a · a 16a = 2 · 2 · 2 · 2 · a 4a(3a + 4)

  18. Factoring Using the (Reverse) Distributive Property • First step is to find the prime factors of each term. • Next step is to find the GCF of the terms in the polynomial. • Now write what is left of each term and leave in parenthesis. Ex) 12a²+ 16a 12a²= 2 · 2 · 3 · a · a 16a = 2 · 2 · 2 · 2 · a 4a(3a + 4) Final Answer 4a(3a + 4)

  19. Another Example: 18cd²+ 12c²d + 9cd

  20. Another Example: 18cd²+ 12c²d + 9cd 18cd² = 2 · 3 · 3 · c · d · d 12c²d = 2 · 2 · 3 · c · c · d 9cd = 3 · 3 · c · d GCF = 3cd Answer: 3cd(6d + 4c + 3)

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