Two questions involving factoring

[erik05]

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

1) $$5x^\frac {1}{2} - 15x^\frac{3}{2}$$


I tried it and got: $$5x^\frac {1}{2} (1-3x)$$
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) $$3(x-6)^2 + 2(x-6)^4 + \frac {3}{x-6}$$

so far I got: $$3(x-6)^3 + 2(x-6)^5 + 3$$ and taking out a common factor of $$(x-6)^3$$ I got: $$(x-6)^3 (3+2(x-6)^2) + 3$$
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) $$5x^\frac {1}{2} - 15x^\frac{3}{2}$$


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

2) $$3(x-6)^2 + 2(x-6)^4 + \frac {3}{x-6}$$

so far I got: $$3(x-6)^3 + 2(x-6)^5 + 3$$ and taking out a common factor of $$(x-6)^3$$ I got: $$(x-6)^3 (3+2(x-6)^2) + 3$$
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:

$$\frac {(x-6)^3 (3+2(x-6)^2) + 3} {x - 6}$$


~~

 

[erik05]

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

 

[scholar]

I have a question. Would it be correct then to simplify it even further by dividing the top $$(x-6)^3$$ with the bottom $$(x-6)$$ to get an answer of $$(x-6)^2 (3+2(x-6)^2)+3$$ 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.