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FACTORING – Common Terms

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FACTORING – Common Terms

Factoring an algebraic expression helps us to simplify the expression. It puts the expression into easier terms for use when dealing with more complicated operations using multiple expressions.

The first thing we need to look at is COMMON TERMS

Common terms are coefficients and / or variables that are SHARED by two or more terms in an expression.

FACTORING – Common Terms

Factoring an algebraic expression helps us to simplify the expression. It puts the expression into easier terms for use when dealing with more complicated operations using multiple expressions.

The first thing we need to look at is COMMON TERMS

Common terms are coefficients and / or variables that are SHARED by two or more terms in an expression.

Let’s look at factoring numbers. What possible combinations of integers make a product ?

FACTORING – Common Terms

Factoring an algebraic expression helps us to simplify the expression. It puts the expression into easier terms for use when dealing with more complicated operations using multiple expressions.

The first thing we need to look at is COMMON TERMS

Common terms are coefficients and / or variables that are SHARED by two or more terms in an expression.

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ?

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ?

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ?

So 12 is divisible by any of these “factors”

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ? What are the factors of 15 ?

So 15 is divisible by any of these “factors”

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ? What are the factors of 15 ?

What “factors” do these numbers share ?

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ? What are the factors of 15 ?

What “factors” do these numbers share ?

FACTORING – Common Terms

The first thing we need to look at is COMMON TERMS

Let’s look at factoring numbers. What possible combinations of integers make a product ?

EXAMPLE : What are the factors of 12 ? What are the factors of 15 ?

We will NEVER use 1, so these two numbers have a COMMON FACTOR of “3”.

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

EXAMPLE : Find the common term between :

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

EXAMPLE : Find the common term between :

OK, what is shared ?

“a” is shared

“b” is not shared

“c” is not shared

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

EXAMPLE : Find the common term between :

OK, what is shared ?

“a” is shared

“b” is not shared

“c” is not shared

What is the smallest exponent of “a” ?

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

EXAMPLE : Find the common term between :

OK, what is shared ?

“a” is shared

“b” is not shared

“c” is not shared

What is the smallest exponent of “a” ?

2 – so a2 is the common term

FACTORING – Common Terms

Using the two previous examples, let’s try some examples that have both shared coefficient factors and variables.

FACTORING – Common Terms

Using the two previous examples, let’s try some examples that have both shared coefficient factors and variables.

EXAMPLE # 1 : Find the common term between :

FACTORING – Common Terms

Using the two previous examples, let’s try some examples that have both shared coefficient factors and variables.

EXAMPLE # 1 : Find the common term between :

What is the highest number that both coefficients are divisible by ?

FACTORING – Common Terms

EXAMPLE # 1 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

FACTORING – Common Terms

EXAMPLE # 1 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Is there a shared variable ?

FACTORING – Common Terms

EXAMPLE # 1 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Is there a shared variable ?

Yes - “x”

FACTORING – Common Terms

EXAMPLE # 1 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Is there a shared variable ?

Yes - “x”

What is the smallest exponent of “x” ?

FACTORING – Common Terms

EXAMPLE # 1 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Is there a shared variable ?

Yes - “x”

What is the smallest exponent of “x” ?

- 2

FACTORING – Common Terms

EXAMPLE # 2 : Find the common term between :

Common Term =

FACTORING – Common Terms

EXAMPLE # 2 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

FACTORING – Common Terms

EXAMPLE # 2 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Are there any shared variables ?

FACTORING – Common Terms

EXAMPLE # 2 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Are there any shared variables ?

YES - “a” and “b”

FACTORING – Common Terms

EXAMPLE # 2 : Find the common term between :

Common Term =

What is the highest number that both coefficients are divisible by ?

Are there any shared variables ?

YES - “a” and “b”

List the smallest exponent of “a” and “b” in your answer…

FACTORING – Common Terms

When factoring an algebraic expression, the first step is always common terms. This example will show how to factor that common term out and get your “factored” answer.

EXAMPLE # 3 : Factor

FACTORING – Common Terms

When factoring an algebraic expression, the first step is always common terms. This example will show how to factor that common term out and get your “factored” answer.

EXAMPLE # 3 : Factor

Common term =

1. Find your common term

FACTORING – Common Terms

When factoring an algebraic expression, the first step is always common terms. This example will show how to factor that common term out and get your “factored” answer.

EXAMPLE # 3 : Factor

Common term =

- Find your common term
- Divide the original terms by the common term. The common term remains in the answer outside parentheses.

FACTORING – Common Terms

EXAMPLE # 3 : Factor

Common term =

- Find your common term
- Divide the original terms by the common term. The common term remains in the answer outside parentheses.

You could check the answer by distributing the common term back into the parentheses and you should get the original problem.

FACTORING – Common Terms

EXAMPLE # 4 : Factor

FACTORING – Common Terms

EXAMPLE # 4 : Factor

Common term =

- Find your common term
- Divide the original terms by the common term. The common term remains in the answer outside parentheses.

FACTORING – Common Terms

EXAMPLE # 4 : Factor

Common term =

- Find your common term

FACTORING – Common Terms

EXAMPLE # 4 : Factor

Common term =