You can
put this solution on YOUR website!# 1
Looking at
we can see that the first term is
and the last term is
where the coefficients are 1 and 14 respectively.
Now multiply the first coefficient 1 and the last coefficient 14 to get 14. Now what two numbers multiply to 14 and add to the middle coefficient -9? Let's list all of the factors of 14:
Factors of 14:
1,2,7,14
-1,-2,-7,-14 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 14
1*14
2*7
(-1)*(-14)
(-2)*(-7)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9
| First Number | Second Number | Sum | | 1 | 14 | 1+14=15 |
| 2 | 7 | 2+7=9 |
| -1 | -14 | -1+(-14)=-15 |
| -2 | -7 | -2+(-7)=-9 |
From this list we can see that -2 and -7 add up to -9 and multiply to 14
Now looking at the expression
, replace
with
(notice
combines 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
)
------------------------------------------------------------
Answer:
So
factors to
# 2
Looking at
we can see that the first term is
and the last term is
where the coefficients are 6 and -4 respectively.
Now multiply the first coefficient 6 and the last coefficient -4 to get -24. Now what two numbers multiply to -24 and add to the middle coefficient -5? Let's list all of the factors of -24:
Factors of -24:
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -24
(1)*(-24)
(2)*(-12)
(3)*(-8)
(4)*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5
| First Number | Second Number | Sum | | 1 | -24 | 1+(-24)=-23 |
| 2 | -12 | 2+(-12)=-10 |
| 3 | -8 | 3+(-8)=-5 |
| 4 | -6 | 4+(-6)=-2 |
| -1 | 24 | -1+24=23 |
| -2 | 12 | -2+12=10 |
| -3 | 8 | -3+8=5 |
| -4 | 6 | -4+6=2 |
From this list we can see that 3 and -8 add up to -5 and multiply to -24
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
)
------------------------------------------------------------
Answer:
So
factors to
(