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Unit 9 – Factoring Polynomials

Unit 9 – Factoring Polynomials. Topic: Greatest Common Factors. Vocabulary. Factor Whole number divisors of another whole number. Ex. 3 is a factor of 27 Variable divisors of another variable. Ex. x 2 is a factor of x 5 Common factors Factors shared by two or more monomials.

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Unit 9 – Factoring Polynomials

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  1. Unit 9 – Factoring Polynomials Topic: Greatest Common Factors

  2. Vocabulary • Factor • Whole number divisors of another whole number. • Ex. 3 is a factor of 27 • Variable divisors of another variable. • Ex. x2 is a factor of x5 • Common factors • Factors shared by two or more monomials. • Ex. 3 is a common factor of 9 and 27 • Greatest Common Factor (GCF) • Largest common factor of two or more monomials. • Ex. 9 is the GCF of 9 & 27

  3. Prime Factorization • Prime number factors of a whole number. • Prime factors can be found using a factor tree. Prime number

  4. Finding GCF of numbers – Listing factors • List factors of each number and identify the GCF. • Example: Find the GCF of 18 and 27. • Factors of 18: 1, 2, 3, 6, 9, 18 • Factors of 27: 1, 3, 9, 27 • GCF = 9

  5. Finding GCF of numbers – Using Factor Trees • Find the prime factors of each number. The GCF will be the product of common primes. • Example: Find the GCF of 18 and 27. • Prime factorization of 18: 2 x 3 x 3 • Prime factorization of 27: 3 x 3 x 3 • Common primes: 3 x 3 • GCF = 9

  6. Finding GCF of variables • GCF will include a common variable base & the lowest exponent of given terms. • Example: Find the GCF of x3, x5y, & x4y2 • Common variable base: x (1st term doesn’t have a y in it) • Lowest exponent of x: 3 • GCF of x3, x5y, & x4y2= x3

  7. Finding GCF of monomials • Must find GCF of coefficients AND variable(s). • Example: Find the GCF of 3x3 and 6x2 • GCF of 3 & 6: 3 • GCF of x3and x2: x2 • GCF of 3x3 & 6x2= 3x2

  8. Factoring polynomials by GCF • Rewriting polynomials as products of monomials & polynomials that cannot be factored further. • Find GCF of the given terms, then factor (divide) it out. • Example: Factor the polynomial • GCF = 5y; divide each term by 5y to find remainders. • NOTE: GCF MUST appear in final answer (Think of factoring as “un-distributing”).

  9. Factoring out a common binomial • Two monomials that are multiplied by the same binomial. • The binomial can be factored out, leaving the two monomials together to form another binomial. • Example: Factor • (x – 2) factors out, leaving 4x & 5 to form a binomial.

  10. Factoring by grouping • Grouping terms of a polynomial by similar GCFs to find a common binomial. • Example: Factor Rewrite the polynomial in standard form, then group the first 2 terms & the last 2 terms. Factor a GCF out of each group (this should give you a common binomial). Factor out the common binomial.

  11. Journal EntryTitle: GCF 3-2-1 • Identify 3 things you already knew from the material in the PowerPoint. • Identify 2 new things you learned. • Identify 1 question you still have.

  12. Homework • Textbook Section 8-1 (p. 527): 16-30 even • Textbook Section 8-2 (p. 535): 28-36 even, 44-54 even • DUE 3/16

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