Unit 9 Factoring Polynomials Topic Greatest Common Factors

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Unit 9 – Factoring Polynomials Topic: Greatest Common Factors

Unit 9 – Factoring Polynomials Topic: Greatest Common Factors

Vocabulary • Factor Ø Whole number divisors of another whole number. Ø Ex. 3

Vocabulary • Factor Ø Whole number divisors of another whole number. Ø Ex. 3 is a factor of 27 Ø Variable divisors of another variable. Ø Ex. x 2 is a factor of x 5 • Common factors Ø Factors shared by two or more monomials. Ø Ex. 3 is a common factor of 9 and 27 • Greatest Common Factor (GCF) Ø Largest common factor of two or more monomials. Ø Ex. 9 is the GCF of 9 & 27

Prime Factorization • Prime number factors of a whole number. Ø Prime factors can

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

Finding GCF of numbers – Listing factors • List factors of each number and

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

Finding GCF of numbers – Using Factor Trees • Find the prime factors of

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. Ø Prime factorization of 18: 2 x 3 Ø Prime factorization of 27: 3 x 3 Ø Common primes: 3 x 3 Ø GCF = 9

Finding GCF of variables • GCF will include a common variable base & the

Finding GCF of variables • GCF will include a common variable base & the lowest exponent of given terms. • Example: Find the GCF of x 3, x 5 y, & x 4 y 2 Ø Common variable base: x (1 st term doesn’t have a y in it) Ø Lowest exponent of x: 3 Ø GCF of x 3, x 5 y, & x 4 y 2= x 3

Finding GCF of monomials • Must find GCF of coefficients AND variable(s). • Example:

Finding GCF of monomials • Must find GCF of coefficients AND variable(s). • Example: Find the GCF of 3 x 3 and 6 x 2 Ø GCF of 3 & 6: 3 Ø GCF of x 3 and x 2: x 2 Ø GCF of 3 x 3 & 6 x 2= 3 x 2

Factoring polynomials by GCF • Rewriting polynomials as products of monomials & polynomials that

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. Ø Example: Factor the polynomial Ø GCF = 5 y; divide each term by 5 y to find remainders. • NOTE: GCF MUST appear in final answer (Think of factoring as “un-distributing”).

Factoring out a common binomial • Two monomials that are multiplied by the same

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. Ø Example: Factor Ø (x – 2) factors out, leaving 4 x & 5 to form a binomial.

Factoring by grouping • Grouping terms of a polynomial by similar GCFs to find

Factoring by grouping • Grouping terms of a polynomial by similar GCFs to find a common binomial. Ø 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.

Journal Entry Title: GCF 3 -2 -1 • Identify 3 things you already knew

Journal Entry Title: GCF 3 -2 -1 • Identify 3 things you already knew from the material in the Power. Point. • Identify 2 new things you learned. • Identify 1 question you still have.

Homework • Textbook Section 8 -1 (p. 527): 16 -30 even • Textbook Section

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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