SOLUTION: Please, having some problems with this one x^3- 26x^2 +48x Thank you ahaead of time.

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Question 117342: Please, having some problems with this one
x^3- 26x^2 +48x
Thank you ahaead of time.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3-26x%5E2%2B48x Start with the given expression


x%28x%5E2-26x%2B48%29 Factor out the GCF x


Now let's focus on the inner expression x%5E2-26x%2B48




Looking at x%5E2-26x%2B48 we can see that the first term is x%5E2 and the last term is 48 where the coefficients are 1 and 48 respectively.

Now multiply the first coefficient 1 and the last coefficient 48 to get 48. Now what two numbers multiply to 48 and add to the middle coefficient -26? Let's list all of the factors of 48:



Factors of 48:
1,2,3,4,6,8,12,16,24,48

-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 48
1*48
2*24
3*16
4*12
6*8
(-1)*(-48)
(-2)*(-24)
(-3)*(-16)
(-4)*(-12)
(-6)*(-8)

note: remember two negative numbers multiplied together make a positive number


Now which of these pairs add to -26? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -26

First NumberSecond NumberSum
1481+48=49
2242+24=26
3163+16=19
4124+12=16
686+8=14
-1-48-1+(-48)=-49
-2-24-2+(-24)=-26
-3-16-3+(-16)=-19
-4-12-4+(-12)=-16
-6-8-6+(-8)=-14



From this list we can see that -2 and -24 add up to -26 and multiply to 48


Now looking at the expression x%5E2-26x%2B48, replace -26x with -2x%2B-24x (notice -2x%2B-24x adds up to -26x. So it is equivalent to -26x)

x%5E2%2Bhighlight%28-2x%2B-24x%29%2B48


Now let's factor x%5E2-2x-24x%2B48 by grouping:


%28x%5E2-2x%29%2B%28-24x%2B48%29 Group like terms


x%28x-2%29-24%28x-2%29 Factor out the GCF of x out of the first group. Factor out the GCF of -24 out of the second group


%28x-24%29%28x-2%29 Since we have a common term of x-2, we can combine like terms



So x%5E2-26x%2B48 factors to %28x-24%29%28x-2%29


x%28x-24%29%28x-2%29 Reintroduce the GCF


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Answer:

So x%5E3-26x%5E2%2B48x factors to x%28x-24%29%28x-2%29