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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 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 ? 1 12 26 3 4 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 ? 1 12 26 3 4 So 12 is divisible by any of these “factors” 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 ? 1 12 26 1 15 35 3 4 So 15 is divisible by any of these “factors” 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 ? 1 12 26 3 4 What are the factors of 15 ? What “factors” do these numbers share ? 1 15 35 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 ? 1 12 26 3 4 What are the factors of 15 ? What “factors” do these numbers share ? 1 15 35 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 ? 1 12 26 3 4 What are the factors of 15 ? 1 15 35 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 : a 2b and a 3c 2 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 : a 2b and a 3c 2 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 : a 2b and a 3c 2 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 : a 2b and a 3c 2 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 : 2 x 4 and 6x2 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 : 2 x 4 and 6x2 What is the highest number that both coefficients are divisible by ? 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 : 2 x 4 and 6x2 Common Term = What is the highest number that both coefficients are divisible by ? 1 2 1 6 23 2 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 : 2 x 4 and 6x2 Common Term = What is the highest number that both coefficients are divisible by ? 1 2 1 6 23 Is there a shared variable ? 2 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 : 2 x 4 and 6x2 Common Term = What is the highest number that both coefficients are divisible by ? 1 2 1 6 23 Is there a shared variable ? Yes - “x” 2 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 : 2 x 4 and 6x2 Common Term = What is the highest number that both coefficients are divisible by ? 1 2 1 6 23 Is there a shared variable ? Yes - “x” What is the smallest exponent of “x” ? 2 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 : 2x 4 and 6x 2 Common Term = What is the highest number that both coefficients are divisible by ? 1 2 1 6 23 Is there a shared variable ? Yes - “x” What is the smallest exponent of “x” ? - 2 2x 2 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 : 3ab3 and 9a 2 b Common Term = 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 : 3ab3 and 9a 2 b Common Term = What is the highest number that both coefficients are divisible by ? 1 3 1 9 33 3 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 : 3ab3 and 9a 2 b Common Term = What is the highest number that both coefficients are divisible by ? 1 3 1 9 33 Are there any shared variables ? 3 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 : 3ab3 and 9a 2 b Common Term = What is the highest number that both coefficients are divisible by ? 1 3 1 9 33 Are there any shared variables ? YES - “a” and “b” 3 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 : 3ab3 and 9a 2 b Common Term = What is the highest number that both coefficients are divisible by ? 1 3 1 9 33 Are there any shared variables ? YES - “a” and “b” List the smallest exponent of “a” and “b” in your answer… 3ab 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 5 x 3 10 x 2 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 5 x 3 10 x 2 Common term = 5x 2 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 5 x 3 10 x 2 Common term = 5x 2 3 2 5 x 10 x 2 5 x 2 2 5 x 2 x 2 5x 5x 1. Find your common term 2. Divide the original terms by the common term. The common term remains in the answer outside parentheses. 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 5 x 3 10 x 2 Common term = 5x 2 3 2 5 x 10 x 2 5 x 2 2 5 x 2 x 2 5x 5x 1. Find your common term 2. 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 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 5ab 5c 2 6a 3bc 4 7a 2b 2 c 3 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 5ab 5c 2 6a 3bc 4 7a 2b 2 c 3 Common term = abc 2 1. Find your common term 2. Divide the original terms by the common term. The common term remains in the answer outside parentheses. 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 5ab 5c 2 6a 3bc 4 7a 2b 2 c 3 Common term = abc 2 5 2 3 4 2 2 3 5 ab c 6 a bc 7 a bc 2 abc 2 2 2 abc abc abc 1. Find your common term 2. Divide the original terms by the common term. The common term remains in the answer outside parentheses. 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 5ab 5c 2 6a 3bc 4 7a 2b 2 c 3 Common term = abc 2 5 2 3 4 2 2 3 5 ab c 6 a bc 7 a bc 2 abc 2 2 2 abc abc abc abc 2 5b 4 6a 2c 2 7abc
