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. 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

Prime Factorization

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

602 30Prime number

2 153 5

5322 5322

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, 18Factors of 27: 1, 3, 9, 27GCF = 9

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 3Prime factorization of 27: 3 x 3 x 3Common primes: 3 x 3GCF = 9

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: 3GCF of x3, x5y, & x4y2= x3

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 x3 and x2: x2

GCF of 3x3 & 6x2= 3x2

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 polynomialGCF = 5y; divide each term by 5y to find

remainders.

• NOTE: GCF MUST appear in final answer (Think of factoring as “un-distributing”).

yyy 52010 23

)142(5 2 yyy

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.

)2(5)2(4 xxx

)54)(2( xx

Factoring by grouping

• Grouping terms of a polynomial by similar GCFs to find a common binomial.Example: Factor 1592012 23 xxx

)34(5)34(3 2 xxx

)1520()912( 23 xxx

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).

)53)(34( 2 xxFactor out the common binomial.

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.

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