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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

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slide1

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.

slide2

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 ?

slide3

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 ?

slide4

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 ?

slide5

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 ?

So 12 is divisible by any of these “factors”

slide6

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 ? What are the factors of 15 ?

So 15 is divisible by any of these “factors”

slide7

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 ? What are the factors of 15 ?

What “factors” do these numbers share ?

slide8

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 ? What are the factors of 15 ?

What “factors” do these numbers share ?

slide9

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 ? What are the factors of 15 ?

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

slide10

FACTORING – Common Terms

Common terms for variables :

- variable has to be shared between ALL terms

- use smallest shared exponent for each shared variable

slide11

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 :

slide12

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

slide13

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” ?

slide14

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

slide15

FACTORING – Common Terms

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

slide16

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 :

slide17

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 ?

slide18

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 :

Common Term =

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

slide19

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 :

Common Term =

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

Is there a shared variable ?

slide20

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 :

Common Term =

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

Is there a shared variable ?

Yes - “x”

slide21

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 :

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” ?

slide22

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 :

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

slide23

FACTORING – Common Terms

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

EXAMPLE # 2 : Find the common term between :

Common Term =

slide24

FACTORING – Common Terms

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

EXAMPLE # 2 : Find the common term between :

Common Term =

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

slide25

FACTORING – Common Terms

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

slide26

FACTORING – Common Terms

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

slide27

FACTORING – Common Terms

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

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

slide28

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

slide29

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

slide30

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.
slide31

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.

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

slide32

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 # 4 : Factor

slide33

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 # 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.
slide34

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 # 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.
slide35

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 # 4 : Factor

Common term =

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