SOLUTION: 24x+2x-12
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Question 127884: 24x+2x-12
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Do you mean ? Do you want to factor?
Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
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Looking at we can see that the first term is and the last term is where the coefficients are 12 and -6 respectively.
Now multiply the first coefficient 12 and the last coefficient -6 to get -72. Now what two numbers multiply to -72 and add to the middle coefficient 1? Let's list all of the factors of -72:
Factors of -72:
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -72
(1)*(-72)
(2)*(-36)
(3)*(-24)
(4)*(-18)
(6)*(-12)
(8)*(-9)
(-1)*(72)
(-2)*(36)
(-3)*(24)
(-4)*(18)
(-6)*(12)
(-8)*(9)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
| First Number | Second Number | Sum | | 1 | -72 | 1+(-72)=-71 |
| 2 | -36 | 2+(-36)=-34 |
| 3 | -24 | 3+(-24)=-21 |
| 4 | -18 | 4+(-18)=-14 |
| 6 | -12 | 6+(-12)=-6 |
| 8 | -9 | 8+(-9)=-1 |
| -1 | 72 | -1+72=71 |
| -2 | 36 | -2+36=34 |
| -3 | 24 | -3+24=21 |
| -4 | 18 | -4+18=14 |
| -6 | 12 | -6+12=6 |
| -8 | 9 | -8+9=1 |
From this list we can see that -8 and 9 add up to 1 and multiply to -72
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
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So our expression goes from and factors further to
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Answer:
So factors to
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