Table of Contents Factoring – General Method You have learned a variety of methods for factoring....

Table of Contents

Factoring – General Method

• You have learned a variety of methods for factoring. This section puts all of the methods together for a general factoring strategy.

• It is very important that you can factor a polynomial without being told what method to use. In fact, sometimes several methods will be used on the same problem.

Table of Contents

• A simple version of the factoring strategy is given below.

1. Always factor the Greatest Common Factor first.

2. Determine how many terms are left in the resulting polynomial.

3. Factor using the methods for that number of terms.

4. After completing a step, always ask, can I factor again?

• This is best described in the following diagram.

Table of Contents

Greatest Common Factor

The Greatest Common Factor is always the first step in factoring.

If you leave this step out, the factoring can get extremely difficult or impossible. Don’t forget the GCF!

Table of Contents


How many terms are there?

Two Three Four

The number of terms determines the possible methods to consider.

Table of Contents


Lets start with two terms.

Two Three Four

The possible factoring methods include …

Difference of Two Squares

Sum of Two Cubes

Difference of Two Cubes

Table of Contents


If there are three terms.

Two Three Four


Sum of Two Cubes


Perfect Square Trinomial

Trinomial: Guess/Check

or ac Method

Table of Contents


If there are four terms.

Two Three Four


Sum of Two Cubes




or ac Method

Grouping

Table of Contents

• Example 1

Factor:

Factor the GCF

35 20x x

25 4x x

Two terms are left in the resulting polynomial

Table of Contents


Two Three Four


Sum of Two Cubes




or ac Method

Grouping

Table of Contents


Two


Sum of Two Cubes


Consider these three methods

Table of Contents

• Example 1

Factor:

Factor the GCF

35 20x x

25 4x x

Two terms are left in the resulting polynomial

It’s a difference of two squares.

5 2 2x x x

Any more factoring possible? No

Table of Contents

• Example 2

Factor:

Factor the GCF

23 24 48x x

23 8 16x x

Three terms are left in the resulting polynomial

Table of Contents


Two Three Four


Sum of Two Cubes




or ac Method

Grouping

Table of Contents


Three



or ac Method

Check for a Perfect Square Trinomial first

Table of Contents

• Example 2

Factor:

Factor the GCF

23 24 48x x

23 8 16x x

Three terms are left in the resulting polynomial

It is a perfect square trinomial.

2 2 4 8ab x x

Table of Contents

23 8 16x x

3 4x

3 4x

23 4x


Table of Contents

• Example 3

Factor:

Factor the GCF

3 22 9 18x x x

Four terms suggests the grouping method.

None, other than 1

3 22 9 18x x x

2 2 9 2x x x

22 9x x

Table of Contents

22 9x x

Any more factoring possible?

Yes, a difference of two squares.

2 3 3x x x


Table of Contents

• With factoring it is important to remember,

after completing a factoring step, always ask

Is there any more factoring possible?

Table of Contents

Table of Contents Factoring – General Method You have learned a variety of methods for factoring....

Documents

Transcript of Table of Contents Factoring – General Method You have learned a variety of methods for factoring....