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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 10 respectively.
Now multiply the first coefficient 3 and the last coefficient 10 to get 30. Now what two numbers multiply to 30 and add to the middle coefficient 17? Let's list all of the factors of 30:
Factors of 30:
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 30
1*30
2*15
3*10
5*6
(-1)*(-30)
(-2)*(-15)
(-3)*(-10)
(-5)*(-6)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 17
| First Number | Second Number | Sum | | 1 | 30 | 1+30=31 |
| 2 | 15 | 2+15=17 |
| 3 | 10 | 3+10=13 |
| 5 | 6 | 5+6=11 |
| -1 | -30 | -1+(-30)=-31 |
| -2 | -15 | -2+(-15)=-17 |
| -3 | -10 | -3+(-10)=-13 |
| -5 | -6 | -5+(-6)=-11 |
From this list we can see that 2 and 15 add up to 17 and multiply to 30
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
(