Two questions involving factoring

[erik05]

Hello all. I have two questions involving factoring and I seem to be stuck.

1) [tex] 5x^\frac {1}{2} - 15x^\frac{3}{2} [/tex]


I tried it and got: [tex] 5x^\frac {1}{2} (1-3x) [/tex]
I'm not too sure if you could go any further than this or if there's another way to approach this. The answer seems too simple and knowing my teacher, there's probably a more complicated one. Any thoughts?

2) [tex] 3(x-6)^2 + 2(x-6)^4 + \frac {3}{x-6} [/tex]

so far I got: [tex] 3(x-6)^3 + 2(x-6)^5 + 3 [/tex] and taking out a common factor of [tex] (x-6)^3 [/tex] I got: [tex] (x-6)^3 (3+2(x-6)^2) + 3 [/tex]
I don't think this can be the simplest form so any suggestions or ideas? Thanks for the help.

 

[xanthym]

Hello all. I have two questions involving factoring and I seem to be stuck.

1) [tex] 5x^\frac {1}{2} - 15x^\frac{3}{2} [/tex]


I tried it and got: [tex] 5x^\frac {1}{2} (1-3x) [/tex]
I'm not too sure if you could go any further than this.

2) [tex] 3(x-6)^2 + 2(x-6)^4 + \frac {3}{x-6} [/tex]

so far I got: [tex] 3(x-6)^3 + 2(x-6)^5 + 3 [/tex] and taking out a common factor of [tex] (x-6)^3 [/tex] I got: [tex] (x-6)^3 (3+2(x-6)^2) + 3 [/tex]
I don't think this can be the simplest form so any suggestions or ideas? Thanks for the help.

#1) CORRECT

#2) You forgot to divide thru by (x - 6) after multiplying by (x - 6) in your first step, so your final answer should be:

[tex] \frac {(x-6)^3 (3+2(x-6)^2) + 3} {x - 6} [/tex]


~~

 

[erik05]

I have a question. Would it be correct then to simplify it even further by dividing the top [tex] (x-6)^3[/tex] with the bottom [tex] (x-6) [/tex] to get an answer of [tex] (x-6)^2 (3+2(x-6)^2)+3 [/tex] or no?

 

[scholar]

I have a question. Would it be correct then to simplify it even further by dividing the top [tex] (x-6)^3[/tex] with the bottom [tex] (x-6) [/tex] to get an answer of [tex] (x-6)^2 (3+2(x-6)^2)+3 [/tex] or no?

It would not be correct to do that because of the +3 on the end.

 

[erik05]

I should learn to look at the question more carefully. Thanks man.