SOLUTION: Factor: (2x^(2/3)) - (5x^(1/3))

SOLUTION: Factor: (2x^(2/3)) - (5x^(1/3)) - 3

Question 148119: Factor: (2x^(2/3)) - (5x^(1/3)) - 3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Let

. This means that

Replace

with

. Replace

with

Looking at we can see that the first term is and the last term is where the coefficients are 2 and -3 respectively.

Now multiply the first coefficient 2 and the last coefficient -3 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

Now replace "z" with

factors to

In other words,

where every variable is positive.
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