The discussion revolves around simplifying a complex fraction involving polynomials: (x² + x - 30) / (2x² + 9x - 10) multiplied by (4x² - 2x) / (x² - 36). Participants are exploring the factoring of these polynomials and identifying potential cancellations.
The conversation is ongoing, with participants providing insights into factoring and cancellations. Some have noted corrections to previous statements, and there is an acknowledgment of the potential for more cancellations based on the correct interpretation of the problem.
There are indications of possible errors in the original problem as presented, leading to confusion about the correct polynomials to factor. Participants are also navigating the challenge of factoring certain expressions and the implications for simplification.
Math Problem said:x² + x - 30 over 2x² + 9x -10 multiplied by 4x² - 2x over x² - 36
-1337- said:Well, I need help solving the next problem:
All you have to do is simplify it. Also, would you be so kind and show your work? Thank you.
It's impossible to factor "2x² + 9x -10" isn't it?topsquark said:[tex]\frac{x^2+x-10}{2x^2+9x-10} \frac{4x^2-2x}{x^2-36}[/tex]
I would start by factoring each polynomial. You will find there are several cancellations.
If this doesn't seem that informative, remember that YOU need to show your work so we can find where you need the help!
-Dan
topsquark said:[tex]\frac{x^2+x-10}{2x^2+9x-10} \frac{4x^2-2x}{x^2-36}[/tex]
I would start by factoring each polynomial. You will find there are several cancellations.
If this doesn't seem that informative, remember that YOU need to show your work so we can find where you need the help!
-Dan
d_leet said:Have you tried to factor any of those? The only 2 that factor don't cancel out.
topsquark said:I can factor all but the [tex]x^2+x-10[/tex]. Usually more cancels out in these problems though.
Take a look at [tex]2x^2+9x-10[/tex]. Since 2 is prime this will factor somehow into a product that looks like [tex]2x^2+9x-10=(2x+a)(x+b)=2x^2+(a+2b)x+ab[/tex]. a and b are factors of 10. What might they be?
-Dan
-1337- said:I'm terribly sorry, it's x² + x - 30, not x² + x -10, but I can factor that. Also, can you explain, please, I have to go to bed soon.
Yes, I'm positive about the 2x² + 9x -10. I guess my teacher didn't write the problem correctly.d_leet said:Well then some more things cancel out, are you sure that it was 2x^2+9x-10 in the original problem because if that's wrong then more things may cancel.
-1337- said:I'm terribly sorry, it's x² + x - 30, not x² + x -10, but I can factor that. Also, can you explain, please, I have to go to bed soon.
-1337- said:Yes, I'm positive about the 2x² + 9x -10. I guess my teacher didn't write the problem correctly.
topsquark said:That helps. Please note the correction I made to my last post. I screwed up and didn't notice before I posted.
I can factor the new polynomial, but still nothing cancels. Are you certain about the 2x^2+9x-10?
-Dan
d_leet said:One thing will cancel. There is a common factor between 2x^2+9x-10 and x^2 - 36.
topsquark said:As you pointed out, 2x^2+9x-10 doesn't factor.
-Dan