Factoring By Grouping - Miami Arts Charter
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Homework AssignmentThe following examples have to be copiedfor next classExample 1Example 5Example 9Example 2Example 6Example 10Example 3Example 7Example 12Example 4Example 8The examples must be copied and ready forme to check once you come to class.Sep 17 4:14 PM1
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Greatest Common Factor(GCF)&Factoring by GroupingJul 24 11:38 AM2
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 1Given the expression :6x – 211. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.6 & 21Factors of 6 : 1, 2, 3, 6Factors of 21 : 1, 3, 7, 21The largest factor that is in each list is 3.GCF(numbers) 3Jul 24 11:41 AM3
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable6x – 211st term has an x which means there is 1 x variable.2nd term does not have an x variablesEach term does NOT have an x variable so there isNO GCF for the x variable.GCF(x variable) noneThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.GCF(expression) 3Jul 24 11:42 AM4
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTION6x – 21GCF 3Place the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 11:42 AM5
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 2Given the expression :–20x 451. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.20 & 45Factors of 20 : 1, 2, 4, 5, 10, 20Factors of 45 : 1, 3, 5, 9, 15, 45The largest factor that is in each list is 5.Next step will only happen if the first term in theexpression is a negative number. I want the GCFand the first term in the expression to have the samesign. Instead of using a positive 5 the GCF will be –5.–20x 45GCF(numbers) –5Jul 24 12:51 PM6
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable–20x 451st term has an x which means there is 1 x variable.2nd term does not have an x variablesEach term does NOT have an x variable so there isNO GCF for the x variable.GCF(x variable) noneThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.GCF(expression) –5Jul 24 12:36 PM7
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTION–20x 45GCF –5Place the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 12:37 PM8
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 3Given the expression :1. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.24 & 8Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24Factors of 8 : 1, 2, 4, 8The largest factor that is in each list is 8.GCF(numbers) 8Jul 24 1:03 PM9
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable1st term has an x which means there is 1 x variable.2nd term has an x2 which means there are 2 x variables.Because each term has at least 1 x variables theGCF for the x variable is x.GCF(x variable) xThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.GCF(expression) 8xJul 24 12:37 PM10
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTIONGCF 8xPlace the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 12:37 PM11
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 4Given the expression :1. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.18 & 27 & 54Factors of 18 : 1, 2, 3, 6, 9, 18Factors of 27 : 1, 3, 9, 27Factors of 18 : 1, 2, 3, 6, 9, 18The largest factor that is in each list is 9.GCF(numbers) 9Jul 24 1:00 PM12
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable1st term has an x3which means there are 3 x variables.2nd term has an x2 which means there are 2 x variables.3rd term has an x4 which means there are 4 x variables.Because each term has at least 2 x variable theGCF for the x variable is x.2GCF(x variable) xThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.GCF(expression) 9x2Jul 24 1:00 PM13
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTIONGCF 9x2Place the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 1:00 PM14
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 5Given the expression :1. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.Factors of 15 : 1, 3, 5, 15Factors of 20 : 1,2,4, 5, 10, 20The largest factor that is in each list is 5.GCF(numbers) 5Jul 24 10:17 AM15
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable1st term has an x2 which means there are 2 x variables.2nd term has an x3 which means there are 3 x variables.Because each term has at least 2 x variables theGCF for the x variable is x2.2GCF(x variable) xJul 24 10:26 AM16
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Repeat the same process with the y variable.1st term has an y2 which means there are 2 y variables.2nd term has a y1 which means there is 1 y variable.Because each term has at least 1 y variable theGCF for the y variable is y.GCF(y variable) yThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.2GCF(expression) 5x yJul 24 10:58 AM17
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTIONGCF 5x2yPlace the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 11:13 AM18
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 6Given the expression :1. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.8 & 14 & 6Factors of 8 : 1, 2, 4, 8Factors of 14 : 1, 2, 7, 14Factors of 6 : 1, 2, 3, 6The largest factor that is in each list is 2.GCF(numbers) 2Jul 24 1:28 PM19
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable1st term has an x3which means there are 3 x variables.2nd term has an x2 which means there are 2 x variables.3rd term has an x which means there is 1 x variable.Because each term has at least 1 x variable theGCF for the x variable is x.GCF(x variable) xJul 24 1:29 PM20
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Repeat the same process with the y variable.1st term has an y2 which means there are 2 y variables.2nd term has a y4 which means there are 4 y variables.3rd term has a y3 which means there are 3 y variables.Because each term has at least 2 y variables theGCF for the y variable is y2.2GCF(y variable) yThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.2GCF(expression) 2xyJul 24 1:29 PM21
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTIONGCF 2xy2Place the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF is distributed to the expression inside theparentheses you will get the original polynomialexpression.Jul 24 1:29 PM22
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 7Given the expression :1. Find the GCF?2. Write an expression that is the product ofthe GCF and another factor.SOLUTION1st find the GCF of all the numbers in thepolynomial expression.6 & 12 & 35Factors of 6 : 1, 2, 3, 6Factors of 12 : 1, 2, 3, 4, 6, 12Factors of 35 : 1, 5, 7, 35The largest factor that is in each list is 1.GCF(numbers) 1Jul 24 2:02 PM23
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172nd find the GCF of each variable in thepolynomial expression.We need to find the variable with the highest exponentthat each term in the polynomial expression has.Start with the x variable1st term has NO x variable.2nd term has an x which means there is 1 x variable.3rd term has an x2 which means there are 2 x variables.Each term does NOT have an x variable so there isNO GCF for the x variable.GCF(x variable) noneJul 24 2:02 PM24
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Repeat the same process with the y variable.1st term has an y2 which means there are 2 y variables.2nd term has an y which means there is 1 y variable.3rd term has NO y variable.Each term does NOT have an y variable so there isNO GCF for the x variable.GCF(y variable) noneThe GCF of the polynomial expression combine theGCF for the numbers and each variable that we found.GCF(expression) 1Jul 24 2:02 PM25
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 20172. Write an expression that is the product ofthe GCF and another factor.SOLUTIONGCF(expression) 1Place the polynomial expression inside of the parentheses,and place the GCF outside of the parentheses. Divide eachterm of the polynomial expression by the GCF.Simplify the expression inside of the parentheses.If the GCF of the expression is 1 then the final answerwill be the original polynomial expression.Jul 24 2:23 PM26
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 8Given the expression factor out the GCF :SOLUTIONFirst find the GCF.GCF 2x –5Place the polynomial expression inside of the brackets,and place the GCF outside of the brackets. Divide eachterm of the polynomial expression by the GCF. Bracketsare being used because the expression already hasparentheses makes it easier to read.Jul 24 2:26 PM27
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 9Given the expression factor out the GCF :SOLUTIONFirst find the GCF.GCF 3y 1Place the polynomial expression inside of the brackets,and place the GCF outside of the brackets. Divide eachterm of the polynomial expression by the GCF. Bracketsare being used because the expression already hasparentheses makes it easier to read.Jul 24 2:26 PM28
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017How to factor a polynomialexpression by GROUPING.1. Check to see if there is a GCF that can befactored out. If there is factor it out of theexpression.2. Make two groups, in most cases the 1st groupwill include the 1st & 2nd terms, and the 2nd groupwill be the 3rd & 4th terms.3. Find the GCF of the 1st group and the 2nd group.4. Factor out the GCF of the 1st group and the 2nd group.5. Find and factor out the GCF of the factoredexpression. (In this step the GCF will always bethe expression inside of the parentheses).Jul 24 2:26 PM29
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 10Factor the expression by grouping :SOLUTIONCheck to see if there is a GCF that can be factoredout. If there is factor it out of the expression.GCF 2xJul 26 12:32 PM30
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Make two groups, in most cases the 1st groupwill include the 1st & 2nd terms, and the 2nd groupwill be the 3rd & 4th terms.stnd1 group2 groupFind the GCF of the 1st group and the 2nd group.2stGCF of the 1 group 4xGCF of the 2ndgroup 5Jul 26 11:08 AM31
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Factor out the GCF of the 1st group and the 2nd group.Find the GCF of the factored expression. (In thisstep the GCF will always be the expression inside of theparentheses).GCF (3x – 7)Jul 26 11:51 AM32
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Factor out the GCF of the factored expression.Jul 26 12:49 PM33
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 11Factor the expression by grouping :SOLUTIONCheck to see if there is a GCF that can be factoredout. If there is factor it out of the expression.GCF 5xJul 26 12:16 PM34
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Make two groups, in most cases the 1st groupwill include the 1st & 2nd terms, and the 2nd groupwill be the 3rd & 4th terms.st1 groupnd2 groupFind the GCF of the 1st group and the 2nd group.GCF of the 1st group 2x2GCF of the 2nd group 3Jul 26 12:16 PM35
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Factor out the GCF of the 1st group and the 2nd group.Find the GCF of the factored expression. (In thisstep the GCF will always be the expression inside of theparentheses).GCF (6x – 1)Jul 26 12:16 PM36
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Factor out the GCF of the factored expression.Jul 26 12:16 PM37
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Example 12Factor the expression by grouping :SOLUTIONCheck to see if there is a GCF that can be factoredout. If there is factor it out of the expression.GCF 1Because the GCF is 1 proceed to the next step.Make two groups, in most cases the 1st groupwill include the 1st & 2nd terms, and the 2nd groupwill be the 3rd & 4th terms.st1 group2nd groupJul 26 12:16 PM38
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Find the GCF of the 1st group and the 2nd group.GCF of the 1st group 5x2GCF of the 2nd group –7The 1st term in the 2nd group is –14 recall from a previous examplethat the GCF and the 1st term in the expression will have the samesign. Instead of using a positive 7 the GCF will be –7.Factor out the GCF of the 1st group and the 2nd group.Jul 26 12:16 PM39
Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebookSeptember 17, 2017Find the GCF of the factored expression. (In thisstep the GCF will always be the expression inside of theparentheses).GCF (2x 3)Factor out the GCF of the factored expression.Jul 26 12:18 PM40
Aug 16, 2017 · Factoring out GCF and by Grouping[In Class Version][Algebra 1].notebook 1 September 17, 2017 Sep 17 4:14 PM Homework Assignment The following examples have to be copied for next class Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 10 Example 12 Example 9
Grouping & Case II Factoring Factoring by Grouping: A new type of factoring is factoring by grouping. This type of factoring requires us to see structure in expressions. We usually factor by grouping when we have a polynomial that has four or more terms. Example Steps x3 2x2 3x 6 1. _ terms together that have
Move to the next page to learn more about factoring and how it relates to polynomials. [page 2] Factoring Trinomials by Grouping There is a systematic approach to factoring trinomials with a leading coefficient greater than 1 called . If you need a refresher on factoring by grouping
Factoring . Factoring. Factoring is the reverse process of multiplication. Factoring polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers. For example, 2 3. 6 Similarly, any
Factoring Polynomials Martin-Gay, Developmental Mathematics 2 13.1 – The Greatest Common Factor 13.2 – Factoring Trinomials of the Form x2 bx c 13.3 – Factoring Trinomials of the Form ax 2 bx c 13.4 – Factoring Trinomials of the Form x2 bx c by Grouping 13.5 – Factoring Perfect Square Trinomials and Difference of Two Squares
241 Algebraic equations can be used to solve a large variety of problems involving geometric relationships. 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring Trinomials of the Form x2 bx c 5.4 Factoring Trinomials of the Form ax2 bx c 5.5 Factoring, Solving Equations, and Problem Solving
Factoring . Factoring. Factoring is the reverse process of multiplication. Factoring polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers. For example, 2 3. 6 Similarly, any
Adding & Subtracting Polynomials Multiplying & Factoring Multiplying Binomials Multiplying Special Cases Factoring x2 bx c Factoring ax2 bx c Factoring Special Cases Factoring by Grouping . Page 3 of 3 Quadratic Functions & Equati
Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping Worksheet #1 Factoring Polynomials: GCF and Factoring by Grouping Find the GCF (greatest common factor) of the expressions. EX 5x2y2, 30x3y EX 2x(x 5), 15(x 5) The GCF is 5x2y The GCF is (x 5) EXERCISES: Find the GCF of the expressions. 1. x2, x6 2. 2 t4 .
