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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 10 respectively.
Now multiply the first coefficient 1 and the last coefficient 10 to get 10. Now what two numbers multiply to 10 and add to the middle coefficient 7? Let's list all of the factors of 10:
Factors of 10:
1,2,5,10
-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 10
1*10
2*5
(-1)*(-10)
(-2)*(-5)
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 | 10 | 1+10=11 |
| 2 | 5 | 2+5=7 |
| -1 | -10 | -1+(-10)=-11 |
| -2 | -5 | -2+(-5)=-7 |
From this list we can see that 2 and 5 add up to 7 and multiply to 10
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
(