Question 173111: So I have a few problems that i cannot figure out. I need to factor these out. The first one is x^2-15wy+3xy-5wx
The second one is 9x^2+2x-8
And the third is 24x^2-10x-4
I really need help with these. I have seen other examples and still can't figure it out. Could you please help me. Thank you.
Found 3 solutions by jim_thompson5910, Alan3354, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
 Start with the given expression
 Rearrange and group like terms.
 Factor the GCF "x" from the first group
 Factor the GCF -5w from the second group
Since we have the common term  we can combine like terms.
 Combine like terms.
So factors to
# 2
Looking at the expression  , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,9,12,18,24,36,72
-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-72)
2*(-36)
3*(-24)
4*(-18)
6*(-12)
8*(-9)
(-1)*(72)
(-2)*(36)
(-3)*(24)
(-4)*(18)
(-6)*(12)
(-8)*(9)
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | -72 | 1+(-72)=-71 | | 2 | -36 | 2+(-36)=-34 | | 3 | -24 | 3+(-24)=-21 | | 4 | -18 | 4+(-18)=-14 | | 6 | -12 | 6+(-12)=-6 | | 8 | -9 | 8+(-9)=-1 | | -1 | 72 | -1+72=71 | | -2 | 36 | -2+36=34 | | -3 | 24 | -3+24=21 | | -4 | 18 | -4+18=14 | | -6 | 12 | -6+12=6 | | -8 | 9 | -8+9=1 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
# 3
 Start with the given expression
 Factor out the GCF
Now let's focus on the inner expression 
------------------------------------------------------------
Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-24)
2*(-12)
3*(-8)
4*(-6)
(-1)*(24)
(-2)*(12)
(-3)*(8)
(-4)*(6)
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| 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 the table, we can see that the two numbers  and add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
So factors to .
------------------------------------------------------------
So our expression goes from and factors further to 
------------------
Answer:
So factors to
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! So I have a few problems that i cannot figure out. I need to factor these out. The first one is x^2-15wy+3xy-5wx
x^2-15wy+3xy-5wx
= (x - 5w)*(x + 3y)
The second one is 9x^2+2x-8
(3x - 2)*(3x + 4)
And the third is 24x^2-10x-4
= 2(12x^2 - 5x - 2)
= 2(3x - 2)*(4x + 1)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! factor these out.
The first one is x^2-15wy+3xy-5wx
Rearrange:
= x^2 - 5wx + 3xy -15wy
= x(x-5w) + 3y(x-5w)
= (x-5w)(x+3y)
============================
The second one is 9x^2+2x-8
x = [-2 +- sqrt(4-4*9*-8)]/18
x = [-2 +- sqrt(292)]/18
x = [ -2 +- 17.088]/18
x = 16.9769 or x = -1.06044...
============================
Cheers,
Stan H.
And the third is 24x^2-10x-4
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