Factoring by Grouping 6.1 Find the Greatest Common Factor (GCF) of - - PowerPoint PPT Presentation

Greatest Common Factor and Factoring by Grouping

6.1

Find the Greatest Common Factor (GCF) of a Set of Terms

Factored form: A number or an expression written as a product of factors. Examples: 2x + 8 = 2(x + 4) x2 + 5x + 6 = (x + 2)(x + 3) Greatest common factor (GCF) of a set of terms: A monomial with the greatest coefficient and degree that evenly divides all of the given terms.

Method

To find the GCF of two or more monomials,

• 1. Write the prime factorization in exponential form

for each monomial.

• 2. Write the GCF’s factorization by including the

prime factors (and variables) common to all the factorizations, each raised to its smallest exponent in the factorizations.

• 3. Multiply the factors in the factorization created in

step 2. Note: If there are no common prime factors, then the GCF is 1.

Exercise 1

Find the GCF [06] 6m4n9, 15mn5 [12] 8(m – n), 11(m – n), m – n

A Method to Find the Prime Factorization of a Constant

Determine how many times two can go into the constant, then the number of threes, fives, sevens, elevens, etc. Example: Factor 420

2 ) 420 2 ) 210 3 ) 105 5 ) 35 7 ) 7 1

There are 2 twos, 1 three, 1 five, 1 seven 420 = 22315171 = 22 3 5 7

Factor a Monomial GCF Out of the Terms of a Polynomial

The method to factor a monomial GCF out of the terms of a polynomial is:

• 1. Find the GCF of all the terms in the

polynomial.

• 2. Rewrite the polynomial as a product of the

GCF and the quotient of the polynomial and the GCF.

Exercise 2

Factor: [20] -2x2y2 - 8x3y + 2xy [30] a( b – 5 ) + 7 ( b – 5 )

Factor Polynomials by Grouping

Method to factor a four-term polynomial by grouping:

2x2 - 4x - 4x + 8

• 1. Factor out any monomial GCF (other than 1) that is

common to all four terms.

• 2. Group together pairs of terms and factor the GCF
• ut of each pair.
• 3. If there is a common binomial factor, then factor it
• ut.
• 4. If there is no common binomial factor, then

interchange the middle two terms and repeat the

• process. If there is still no common binomial factor,

then the polynomial cannot be factored by grouping.

Exercise 3

Factor: [50] 15 c3 – 5 c2d + 6 cd2 – 2 d3 [62] 12 ac + 12 cx - 3 ac2 - 3 c2x [**] 2x3 – y3 – 2x2y + xy2

Greatest Common Factor and Factoring by Grouping

6.1