Download Factoring Chapter 5 Chapter 5-1 Copyright © 2015, 2011, 2007 Pearson Education, Inc.

Chapter 5
Factoring
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-1
Chapter Sections
5.1 – Factoring a Monomial from a Polynomial
5.2 – Factoring by Grouping
5.3 – Factoring Trinomials of the Form
ax2 + bx + c, a = 1
5.4 – Factoring Trinomials of the Form
ax2 + bx + c, a ≠ 1
5.5 – Special Factoring Formulas and a General Review
of Factoring
5.6 – Solving Quadratic Equations Using Factoring
5.7 – Applications of Quadratic Equations
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-2
2
Factoring a Monomial
from a Polynomial
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-3
3
Factors
To factor an expression means to write the
expression as a product of its factors.
If a · b = c, then a and b are factors
of c.
a·b
Recall that the greatest common factor (GCF) of
two or more numbers is the greatest number that will
divide (without remainder) into all the numbers.
Example: The GCF of 27 and 45 is 9.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-4
4
Factors
A prime number is an integer greater than 1 that has
exactly two factors, 1 and itself.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
A composite number is an integer greater than 1 that
is not prime. The first 15 composite numbers are:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25
The number 1 is neither prime nor composite.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-5
5
Factors
Prime factorization is used to write a number as a
product of its primes.
48 = 2 · 2 · 2 · 2 · 3
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Chapter 5-6
6
Determining the GCF
1. Write each number as a product of prime
factors.
2. Determine the prime factors common to all
the numbers.
3. Multiply the common factors found in step 2.
The product of these factors is the GCF.
Example: Determine the GCF of 48 and 60.
48 = 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
Two factors of 2 and a factor of 3 are common to both,
therefore 2 · 2· 3 = 12 is the GCF.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-7
7
Determining the GCF
To determine the GCF of two or more terms, take
each factor the largest number of times it appears in
all of the terms.
Example:
a.) Determine the GCF of the terms m9, m5, m7, and m4
The GDF is m4 because m4 is the largest factor
common to all the terms.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-8
8
Determining the GCF of Two or More Terms
1. Find the GCF of the numerical coefficients of
the terms.
2. Find the largest power of each variable that is
common to all of the terms.
3. The GCF is the product of the number from
step 1 and the variable expressions from step 2.
Example: Determine the GCF of 18y2, 15y3, 27y5.
The GCF of 18, 15, and 27 is 3. The GCF of y2, y3, and
y5 is y2. Therefore, the GCF of the three terms is 3y2.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-9
9
Factoring Monomials from Polynomials
1. Determine the GCF of all the terms in the
polynomial.
2. Write each term as the product of the GCF
and its other factor.
3. Use the distributive property to factor out
the GCF.
Example: 6x + 18 (GCF is 6)
= 6·x + 6·3 = 6 (x+ 3)
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 5-10
10