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 4 and 5 respectively.
Now multiply the first coefficient 4 and the last coefficient 5 to get 20. Now what two numbers multiply to 20 and add to the middle coefficient -12? Let's list all of the factors of 20:
Factors of 20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 20
1*20
2*10
4*5
(-1)*(-20)
(-2)*(-10)
(-4)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12
| First Number | Second Number | Sum | | 1 | 20 | 1+20=21 |
| 2 | 10 | 2+10=12 |
| 4 | 5 | 4+5=9 |
| -1 | -20 | -1+(-20)=-21 |
| -2 | -10 | -2+(-10)=-12 |
| -4 | -5 | -4+(-5)=-9 |
From this list we can see that -2 and -10 add up to -12 and multiply to 20
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
#2
Looking at
we can see that the first term is
and the last term is
where the coefficients are 3 and -2 respectively.
Now multiply the first coefficient 3 and the last coefficient -2 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient -5? Let's list all of the factors of -6:
Factors of -6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -6
(1)*(-6)
(2)*(-3)
(-1)*(6)
(-2)*(3)
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 | -6 | 1+(-6)=-5 |
| 2 | -3 | 2+(-3)=-1 |
| -1 | 6 | -1+6=5 |
| -2 | 3 | -2+3=1 |
From this list we can see that 1 and -6 add up to -5 and multiply to -6
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
#3
Looking at
we can see that the first term is
and the last term is
where the coefficients are 3 and -6 respectively.
Now multiply the first coefficient 3 and the last coefficient -6 to get -18. Now what two numbers multiply to -18 and add to the middle coefficient 7? Let's list all of the factors of -18:
Factors of -18:
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -18
(1)*(-18)
(2)*(-9)
(3)*(-6)
(-1)*(18)
(-2)*(9)
(-3)*(6)
note: remember, the product of a negative and a positive number is a negative 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 | -18 | 1+(-18)=-17 |
| 2 | -9 | 2+(-9)=-7 |
| 3 | -6 | 3+(-6)=-3 |
| -1 | 18 | -1+18=17 |
| -2 | 9 | -2+9=7 |
| -3 | 6 | -3+6=3 |
From this list we can see that -2 and 9 add up to 7 and multiply to -18
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
(