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Looking at
we can see that the first term is
and the last term is
where the coefficients are 1 and -28 respectively.
Now multiply the first coefficient 1 and the last coefficient -28 to get -28. Now what two numbers multiply to -28 and add to the middle coefficient 3? Let's list all of the factors of -28:
Factors of -28:
1,2,4,7,14,28
-1,-2,-4,-7,-14,-28 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -28
(1)*(-28)
(2)*(-14)
(4)*(-7)
(-1)*(28)
(-2)*(14)
(-4)*(7)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3
| First Number | Second Number | Sum | | 1 | -28 | 1+(-28)=-27 |
| 2 | -14 | 2+(-14)=-12 |
| 4 | -7 | 4+(-7)=-3 |
| -1 | 28 | -1+28=27 |
| -2 | 14 | -2+14=12 |
| -4 | 7 | -4+7=3 |
From this list we can see that -4 and 7 add up to 3 and multiply to -28
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
(