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FACTORING – Common TermsPowerPoint Presentation

FACTORING – Common Terms

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Presentation Transcript

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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 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 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 ?

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 ?

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”

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”

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 ?

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 ?

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”.

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

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 :

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

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” ?

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

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

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 :

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 ?

EXAMPLE # 1 : Find the common term between :

Common Term =

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

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 ?

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”

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” ?

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

EXAMPLE # 2 : Find the common term between :

Common Term =

EXAMPLE # 2 : Find the common term between :

Common Term =

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

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 ?

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”

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…

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

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

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.

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.

EXAMPLE # 4 : Factor

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.

EXAMPLE # 4 : Factor

Common term =

- Find your common term

EXAMPLE # 4 : Factor

Common term =

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