Factoring

1
Factoring

• Greatest Common Factor
• The largest common factor in all the terms of the
  polynomial

2
Example

• pg. 342, 9

3
Factoring by GroupingSee page 341
4
Example

• Factor (mx 3qxmy3qy)
• We will take the terms in pairs
• The GCF of mx and 3qx is x
• The GCF of my and 3qy is y

5
Example 39 on page 342

• Factor mx 3qxmy3qy
• Step 1 Use GCF in pairs x(m3q) y( m3q)
• Step 2 Notice or look for any common factors
• x(m3q) y( m3q)
• Step 3 Factoring out the common factors yields
• The factored form is (m3q)(xy)

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Special Factorizations
7
Strategy forFactoring Polynomials
8
Solving Equations by Factoring
9
Solve the equationSee page 366 18
10
The Plan

• Distribute (FOIL) the left hand side (LHS)
• Distribute the right hand side (RHS)
• Gather all terms on the RHS, setting the LHS
  equal to 0
• Factor ( if possible) the LHS
• Apply the Zero-Factor Property to Solve (see page
  360)
• Check our solution in the ORIGINAL Problem

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Distribute on RHS and LHS
12
Gather all terms on the LHS, setting the RHS
equal to 0
13
Factor ( if possible) the LHS

• Remember that we must use trial and error to find
  the factors until we exhaust all possibilities

14
Apply the Zero-Factor Property to Solve
15
The Check

16
The Check continued
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Solving a Quadratic Equation by Factoring Overview

• Step 1 Use algebraic properties to ensure that
  one side is equal to 0
• Step 2 Factor this polynomial
• Step 3 Use the zero-factor property by setting
  each of the factors equal to 0
• Step 4 Solve each of the equations from step 3
  independently
• Step 5 Check solution in the original problem

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Good Luck!

• Only three chapters away from completing the
  course.