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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 9 respectively.
Now multiply the first coefficient 1 and the last coefficient 9 to get 9. Now what two numbers multiply to 9 and add to the middle coefficient 6? Let's list all of the factors of 9:
Factors of 9:
1,3
-1,-3 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 9
1*9
3*3
(-1)*(-9)
(-3)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 6
| First Number | Second Number | Sum | | 1 | 9 | 1+9=10 |
| 3 | 3 | 3+3=6 |
| -1 | -9 | -1+(-9)=-10 |
| -3 | -3 | -3+(-3)=-6 |
From this list we can see that 3 and 3 add up to 6 and multiply to 9
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
)
note:
is equivalent to
since the term
occurs twice. So
also factors to
-------------------------------
Answer:
So
factors to
#2
Looking at
we can see that the first term is
and the last term is
where the coefficients are 9 and 1 respectively.
Now multiply the first coefficient 9 and the last coefficient 1 to get 9. Now what two numbers multiply to 9 and add to the middle coefficient -6? Let's list all of the factors of 9:
Factors of 9:
1,3
-1,-3 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 9
1*9
3*3
(-1)*(-9)
(-3)*(-3)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6
| First Number | Second Number | Sum | | 1 | 9 | 1+9=10 |
| 3 | 3 | 3+3=6 |
| -1 | -9 | -1+(-9)=-10 |
| -3 | -3 | -3+(-3)=-6 |
From this list we can see that -3 and -3 add up to -6 and multiply to 9
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
)
note:
is equivalent to
since the term
occurs twice. So
also factors to
-------------------------------
Answer:
So
factors to
(