SOLUTION: I'm taking an online class and the book does not give a very good explanation on how to do the following problem: Please help. Factor, using the given factor. Assume all variabl

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I'm taking an online class and the book does not give a very good explanation on how to do the following problem: Please help. Factor, using the given factor. Assume all variabl      Log On


   

Question 48555: I'm taking an online class and the book does not give a very good explanation on how to do the following problem: Please help.
Factor, using the given factor. Assume all variables represent positive real numbers.
2k^-3 + k^-8 ; k^-8
Found 2 solutions by josmiceli, AnlytcPhil:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2k%5E%28-3%29+%2B+k%5E%28-8%29
note that k%5E%28-3%29+=+k%5E5+%2A+k%5E%28-8%29
2k%5E5%2Ak%5E%28-8%29+%2B+k%5E%28-8%29
factor out k%5E%28-8%29
k%5E%28-8%29%2A%282k%5E5+%2B+1%29 answer

Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
Factor, using the given factor. Assume all variables 
represent positive real numbers.

2k-3 + k-8 ; k-8 

It means to put the k-8 on the left, followed 
by an open parentheses with a couple blanks and
a + sign between like this:

k-8(    +    )    
    ŻŻŻ   ŻŻ
and then fill in those two blanks in the parentheses 
with two terms such that if you were to distribute it
out you would get the original expression 2k-3 + k-8.

To find out what goes in the first blank divide 2k-3 
by k-8 by subtracting exponents -3 MINUS -8.  Do that 
out to the side or on scrap paper, like this

(-3) - (-8) =  -3 + 8 = 5   

then write 2k5 in the first blank

k-8(2k5 +    )
    ŻŻŻ   ŻŻ
To find out what goes in the second blank divide 2k-8 by
k-8 by subtracting exponents -8 MINUS -8.  Do that out to 
the side or on scrap paper, like this

(-8) - (-8) =  -8 + 8 = 0 

So that means k0 goes in the second blank.

k-8(2k5 + k0 )
    ŻŻŻ   ŻŻ

But k0 is just 1, so we erase the k0 and put a 1 there

k-8(2k5 +  1 )
    ŻŻŻ   ŻŻ
Answer:

k-8(2k5 + 1)

Edwin