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Looking at
we can see that the first term is
and the last term is
where the coefficients are 3 and 5 respectively.
Now multiply the first coefficient 3 and the last coefficient 5 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 8? Let's list all of the factors of 15:
Factors of 15:
1,3,5,15
-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 15
1*15
3*5
(-1)*(-15)
(-3)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8
| First Number | Second Number | Sum | | 1 | 15 | 1+15=16 |
| 3 | 5 | 3+5=8 |
| -1 | -15 | -1+(-15)=-16 |
| -3 | -5 | -3+(-5)=-8 |
From this list we can see that 3 and 5 add up to 8 and multiply to 15
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
(