# Thread: Factoring an expression that results from using the "product rule"

1. ## Factoring an expression that results from using the "product rule"

I would really love some help factoring this expression. I've been able to understand factoring up until the point where the 1/2 and -1/2 powers come in.

3(2x-1)(2) (x+3)∕ + (2x-1) (1/2) (x+3)-∕

2. Originally Posted by Hopee
I would really love some help factoring this expression. I've been able to understand factoring up until the point where the 1/2 and -1/2 powers come in.

3(2x-1)(2) (x+3)∕ + (2x-1) (1/2) (x+3)-∕
$\displaystyle (x+3)^{1/2} = \sqrt{x+3}$

$\displaystyle (x+3)^{-\frac {1}{2}} =\frac {1}{ \sqrt{x+3} }$

does this helps you ?

3. I'm curious about a character display issue I'm having. Under Vista Home Premium SP1 with Firefox 3.6.8 I see

But I'm guessing it's displayed properly on other systems/browsers? Anybody have more info or can offer screenshots?

4. Originally Posted by undefined
I'm curious about a character display issue I'm having. Under Vista Home Premium SP1 with Firefox 3.6.8 I see

But I'm guessing it's displayed properly on other systems/browsers? Anybody have more info or can offer screenshots?

$\displaystyle 3(2x-1)^2 (2)(x+3)^{\frac{1}{2}} + (2x-1)^3 (\frac {1}{2}) (x+3)^{-\frac {1}{2}}$

that's what i see

5. Originally Posted by yeKciM
$^\displaystyle 3(2x-1)^2 (2)(x+3)^{\frac{1}{2}} + (2x-1)^3 (\frac {1}{2}) (x+3)^{-\frac {1}{2}}$

that's what i see
Would you mind telling me what OS and browser you are using?

I do some web design so it's useful to know things like this.

6. Originally Posted by undefined
Would you mind telling me what OS and browser you are using?

I do some web design so it's useful to know things like this.
right now XPsp2 (google chrome) but mostly linux

7. I'm on XP SP2 with chrome as well and I have the same issue as you, undefined.

8. here's how i see that

9. Well I understand that 1/2 power is a square root to the one power, I've just never factored anything with a 1/2 or -1/2 power before and I think I just need to see it done once. Not sure how like terms factor out in this situation I guess.

10. $\displaystyle 3(2x-1)^2 (2)(x+3)^{\frac{1}{2}} + (2x-1)^3 (\frac {1}{2}) (x+3)^{-\frac {1}{2}}$

$\displaystyle 3(2x-1)^2 (2)\sqrt{(x+3)} + \frac {(2x-1)^3}{2\sqrt{(x+3)}}$

$\displaystyle \frac {(3(2x-1)^2(2)\sqrt{(x+3)})(2\sqrt{(x+3)}) +(2x-1)^3} {2\sqrt{(x+3)}}$

$\displaystyle \frac {3(2x-1)^2(4)(x+3) +(2x-1)^3} {2\sqrt{(x+3)}}$

$\displaystyle \frac {(2x-1)^2 ( (12)(x+3) +(2x-1))} {2\sqrt{(x+3)}}$

....... can you continue ?

11. Yes, Thank you so much for your help~!

12. For anyone interested in the side topic of character display issues, I have uncovered some preliminary information.

The numbers in the box give a hex code for a UTF-8 encoded character. F0 07 means 0xf007 which in decimal is 61447 which you can see if you view the source code, where it appears as & 61447; without the space after the ampersand.

I'm still trying to see why my system/browser does not display the characters. Relevant links are

general UTF-8 stress test: UTF-8 Sampler (most display fine on my system, but some, like runes at the beginning, do not)

UTF-8 characters in the range 61400-61500: Full UTF-8 Character Map Generator (none of which displays properly with my setup)

Edit: The server for the second link seems to be having issues at the moment, but you can find similar sites with internet search.

Update: Seems to be a font issue. For example when I installed Code2000 I was able to view the runes. Presumably with the right font I will be able to view 0xf007 etc. Possibly it's because I don't have MS Office which comes bundled with some fonts.

13. Hmm haven't found a font that displays those characters yet. If anyone who sees them properly wants to help me out, you can go here (need JavaScript enabled)

Local Font List

and report for what font(s) it is displayed properly..

14. My Professor doesn't let us use roots for the most part but requires everything in fractions. This is what I got as a factor for this equation and finally figured out how to copy paste from MathType so the funny characters don't show up. I'm very new to math forums but learning.

$\begin{array}{l}
3{(2x - 1)^2}(2){(x + 3)^{1/2}} + {(2x - 1)^3}(\frac{1}{2}){(x + 3)^{ - 1/2}}\\
{(2x - 1)^2}{(x + 3)^{ - 1/2}}[3(2)(x + 3) + \frac{1}{2}(2x - 1)]\\
{(2x - 1)^2}{(x - 3)^{ - 1/2}}[6x + 18 + x - \frac{1}{2}]\\
{(2x - 1)^2}{(x - 3)^{ - 1/2}}[7x + 17\frac{1}{2}]
\end{array}$