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Looking at
we can see that the first term is
and the last term is
where the coefficients are 6 and 2 respectively.
Now multiply the first coefficient 6 and the last coefficient 2 to get 12. Now what two numbers multiply to 12 and add to the middle coefficient 7? Let's list all of the factors of 12:
Factors of 12:
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 12
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7
| First Number | Second Number | Sum | | 1 | 12 | 1+12=13 |
| 2 | 6 | 2+6=8 |
| 3 | 4 | 3+4=7 |
| -1 | -12 | -1+(-12)=-13 |
| -2 | -6 | -2+(-6)=-8 |
| -3 | -4 | -3+(-4)=-7 |
From this list we can see that 3 and 4 add up to 7 and multiply to 12
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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Answer:
So
factors to
(