Factoring by Grouping - Miami Arts Charter...2017/08/16 · Factoring out GCF and by Grouping[In...
Transcript of Factoring by Grouping - Miami Arts Charter...2017/08/16 · Factoring out GCF and by Grouping[In...
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
1
September 17, 2017
Sep 174:14 PM
Homework Assignment
The following examples have to be copied for next class
Example 1
Example 2
Example 3
Example 4
Example 5
Example 10 Example 6
Example 12
Example 9
The examples must be copied and ready for me to check once you come to class.
Example 7
Example 8
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
2
September 17, 2017
Jul 2411:38 AM
Greatest Common Factor(GCF)
Factoring by Grouping
&
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
3
September 17, 2017
Jul 2411:41 AM
Example 1
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 6 : 1, 2, 3, 6
Factors of 21 : 1, 3, 7, 21
The largest factor that is in each list is 3.
6x – 21
6 & 21
GCF(numbers) = 3
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
4
September 17, 2017
Jul 2411:42 AM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
1st term has an x which means there is 1 xvariable.
2nd term does not have an xvariables
Each term does NOT have an xvariable so there is NO GCF for the xvariable.
6x – 21
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
GCF(xvariable) = none
GCF(expression) = 3
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
5
September 17, 2017
Jul 2411:42 AM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
6x – 21GCF = 3
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
6
September 17, 2017
Jul 2412:51 PM
Example 2
SOLUTION
1. Find the GCF?
Given the expression : –20x + 45
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 20 : 1, 2, 4, 5, 10, 20
Factors of 45 : 1, 3, 5, 9, 15, 45
The largest factor that is in each list is 5.
20 & 45
Next step will only happen if the first term in the expression is a negative number. I want the GCF and the first term in the expression to have the same sign. Instead of using a positive 5 the GCF will be –5.
–20x + 45
GCF(numbers) = –5
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
7
September 17, 2017
Jul 2412:36 PM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
1st term has an x which means there is 1 xvariable.
2nd term does not have an xvariables
Each term does NOT have an xvariable so there is NO GCF for the xvariable.
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
–20x + 45
GCF(xvariable) = none
GCF(expression) = –5
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
8
September 17, 2017
Jul 2412:37 PM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
–20x + 45GCF = –5
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
9
September 17, 2017
Jul 241:03 PM
Example 3
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24
Factors of 8 : 1, 2, 4, 8
The largest factor that is in each list is 8.
24 & 8
GCF(numbers) = 8
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
10
September 17, 2017
Jul 2412:37 PM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
1st term has an x which means there is 1 xvariable.
2nd term has an x2 which means there are 2 xvariables.
Because each term has at least 1 xvariables the GCF for the xvariable is x.
GCF(xvariable) = x
GCF(expression) = 8x
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
11
September 17, 2017
Jul 2412:37 PM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
GCF = 8x
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
12
September 17, 2017
Jul 241:00 PM
Example 4
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 18 : 1, 2, 3, 6, 9, 18
The largest factor that is in each list is 9.
18 & 27 & 54
Factors of 27 : 1, 3, 9, 27
Factors of 18 : 1, 2, 3, 6, 9, 18
GCF(numbers) = 9
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
13
September 17, 2017
Jul 241:00 PM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
2nd term has an x2 which means there are 2 xvariables.
Because each term has at least 2 xvariable the GCF for the xvariable is x.
1st term has an x3which means there are 3 xvariables.
3rd term has an x4 which means there are 4 xvariables.
GCF(xvariable) = x2
GCF(expression) = 9x2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
14
September 17, 2017
Jul 241:00 PM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
GCF = 9x2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
15
September 17, 2017
Jul 2410:17 AM
Example 5
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 15 : 1, 3, 5, 15
Factors of 20 : 1,2,4, 5, 10, 20
The largest factor that is in each list is 5.
GCF(numbers) = 5
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
16
September 17, 2017
Jul 2410:26 AM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
1st term has an x2 which means there are 2 xvariables.
2nd term has an x3 which means there are 3 xvariables.
Because each term has at least 2 xvariables the GCF for the xvariable is x2.
GCF(xvariable) = x2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
17
September 17, 2017
Jul 2410:58 AM
Repeat the same process with the y variable.
2nd term has a y1 which means there is 1 yvariable.
1st term has an y2 which means there are 2 yvariables.
Because each term has at least 1 yvariable the GCF for the yvariable is y.
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
GCF(yvariable) = y
GCF(expression) = 5x2y
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
18
September 17, 2017
Jul 2411:13 AM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
GCF = 5x2yPlace the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
19
September 17, 2017
Jul 241:28 PM
Example 6
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 8 : 1, 2, 4, 8
The largest factor that is in each list is 2.
8 & 14 & 6
Factors of 14 : 1, 2, 7, 14
Factors of 6 : 1, 2, 3, 6
GCF(numbers) = 2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
20
September 17, 2017
Jul 241:29 PM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
GCF(xvariable) = x
2nd term has an x2 which means there are 2 xvariables.
Because each term has at least 1 xvariable the GCF for the xvariable is x.
1st term has an x3which means there are 3 xvariables.
3rd term has an x which means there is 1 xvariable.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
21
September 17, 2017
Jul 241:29 PM
Repeat the same process with the y variable.
2nd term has a y4 which means there are 4 yvariables.
1st term has an y2 which means there are 2 yvariables.
Because each term has at least 2 yvariables the GCF for the yvariable is y2.
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
3rd term has a y3 which means there are 3 yvariables.
GCF(yvariable) = y2
GCF(expression) = 2xy2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
22
September 17, 2017
Jul 241:29 PM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
Simplify the expression inside of the parentheses.
If the GCF is distributed to the expression inside the parentheses you will get the original polynomial expression.
GCF = 2xy2
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
23
September 17, 2017
Jul 242:02 PM
Example 7
SOLUTION
1. Find the GCF?
Given the expression :
Write an expression that is the product of the GCF and another factor.
2.
1st find the GCF of all the numbers in the polynomial expression.
Factors of 6 : 1, 2, 3, 6
The largest factor that is in each list is 1.
6 & 12 & 35
Factors of 12 : 1, 2, 3, 4, 6, 12
Factors of 35 : 1, 5, 7, 35
GCF(numbers) = 1
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
24
September 17, 2017
Jul 242:02 PM
2nd find the GCF of each variable in the polynomial expression.
We need to find the variable with the highest exponent that each term in the polynomial expression has.
Start with the x variable
3rd term has an x2 which means there are 2 xvariables.
1st term has NO xvariable.
2nd term has an x which means there is 1 xvariable.
Each term does NOT have an xvariable so there is NO GCF for the xvariable.
GCF(xvariable) = none
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
25
September 17, 2017
Jul 242:02 PM
Repeat the same process with the y variable.
1st term has an y2 which means there are 2 yvariables.
The GCF of the polynomial expression combine the GCF for the numbers and each variable that we found.
GCF(expression) = 1
Each term does NOT have an yvariable so there is NO GCF for the xvariable.
GCF(yvariable) = none
2nd term has an y which means there is 1 yvariable.
3rd term has NO yvariable.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
26
September 17, 2017
Jul 242:23 PM
Write an expression that is the product of the GCF and another factor.
2.
SOLUTION
Place the polynomial expression inside of the parentheses, and place the GCF outside of the parentheses. Divide each term of the polynomial expression by the GCF.
GCF(expression) = 1
Simplify the expression inside of the parentheses.
If the GCF of the expression is 1 then the final answer will be the original polynomial expression.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
27
September 17, 2017
Jul 242:26 PM
Example 8
SOLUTION
GCF = 2x – 5
First find the GCF.
Place the polynomial expression inside of the brackets, and place the GCF outside of the brackets. Divide each term of the polynomial expression by the GCF. Brackets are being used because the expression already has parentheses makes it easier to read.
Given the expression factor out the GCF :
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
28
September 17, 2017
Jul 242:26 PM
Example 9
SOLUTION
GCF = 3y + 1First find the GCF.
Place the polynomial expression inside of the brackets, and place the GCF outside of the brackets. Divide each term of the polynomial expression by the GCF. Brackets are being used because the expression already has parentheses makes it easier to read.
Given the expression factor out the GCF :
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
29
September 17, 2017
Jul 242:26 PM
How to factor a polynomial expression by GROUPING.
Make two groups, in most cases the 1st group will include the 1st & 2nd terms, and the 2nd group will be the 3rd & 4th terms.
Find and factor out the GCF of the factored expression. (In this step the GCF will always be the expression inside of the parentheses).
1.
2.
3.
4.
5.
Check to see if there is a GCF that can be factored out. If there is factor it out of the expression.
Find the GCF of the 1st group and the 2nd group.
Factor out the GCF of the 1st group and the 2nd group.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
30
September 17, 2017
Jul 2612:32 PM
Example 10
SOLUTION
Factor the expression by grouping :
GCF = 2x
Check to see if there is a GCF that can be factored out. If there is factor it out of the expression.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
31
September 17, 2017
Jul 2611:08 AM
1st group 2nd group
Make two groups, in most cases the 1st group will include the 1st & 2nd terms, and the 2nd group will be the 3rd & 4th terms.
Find the GCF of the 1st group and the 2nd group.
GCF of the 1st group = 4x2
GCF of the 2nd group = 5
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
32
September 17, 2017
Jul 2611:51 AM
Factor out the GCF of the 1st group and the 2nd group.
Find the GCF of the factored expression. (In this step the GCF will always be the expression inside of the parentheses).
GCF = (3x – 7)
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
33
September 17, 2017
Jul 2612:49 PM
Factor out the GCF of the factored expression.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
34
September 17, 2017
Jul 2612:16 PM
Example 11
SOLUTION
Factor the expression by grouping :
Check to see if there is a GCF that can be factored out. If there is factor it out of the expression.
GCF = 5x
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
35
September 17, 2017
Jul 2612:16 PM
1st group 2nd group
Make two groups, in most cases the 1st group will include the 1st & 2nd terms, and the 2nd group will be the 3rd & 4th terms.
Find the GCF of the 1st group and the 2nd group.
GCF of the 1st group = 2x2
GCF of the 2nd group = 3
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
36
September 17, 2017
Jul 2612:16 PM
Factor out the GCF of the 1st group and the 2nd group.
Find the GCF of the factored expression. (In this step the GCF will always be the expression inside of the parentheses).
GCF = (6x – 1)
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
37
September 17, 2017
Jul 2612:16 PM
Factor out the GCF of the factored expression.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
38
September 17, 2017
Jul 2612:16 PM
Example 12
SOLUTION
Factor the expression by grouping :
GCF = 1
Check to see if there is a GCF that can be factored out. If there is factor it out of the expression.
Because the GCF is 1 proceed to the next step.
Make two groups, in most cases the 1st group will include the 1st & 2nd terms, and the 2nd group will be the 3rd & 4th terms.
1st group 2nd group
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
39
September 17, 2017
Jul 2612:16 PM
Find the GCF of the 1st group and the 2nd group.
GCF of the 1st group = 5x2
GCF of the 2nd group = –7
The 1st term in the 2nd group is –14 recall from a previous example that the GCF and the 1st term in the expression will have the same sign. Instead of using a positive 7 the GCF will be –7.
Factor out the GCF of the 1st group and the 2nd group.
Factoring out GCF and by Grouping[InClass Version][Algebra 1].notebook
40
September 17, 2017
Jul 2612:18 PM
Find the GCF of the factored expression. (In this step the GCF will always be the expression inside of the parentheses).
GCF = (2x + 3)
Factor out the GCF of the factored expression.