Though I am doing well in Algebra, I cannot solve such problems... D:

http://archive.org/stream/mathematicalprob00wolsuoft#page/12/mode/2up

Question

Though I am doing well in Algebra, I cannot solve such problems... D:

http://archive.org/stream/mathematicalprob00wolsuoft#page/12/mode/2up

anonymous · Answer

So start with number 1:

Simplify $\dfrac{11x^4+24x^3+125}{x^4+24x+25}$

I don't know where to start D:

anonymous · Answer

me neither

anonymous · Answer

apparently you can factor and cancel 
btw you have a typo there, it should be $$\dfrac{11x^4+24x^3+125}{x^4+24x+55}$$

anonymous · Answer

Ohh, right. but still, I don't know how to factor such polynomial...

Have any idea?

anonymous · Answer

no
i am thinking it is some sort of completing the square trick 
adding and subtracting , but i do not see it

coconutjj · Answer

Factor Theorem would work

anonymous · Answer

I did a quick research on this theorem, it seems that I need to make trial and error to find factor. Judging from given expression, I would have to go through several numbers :/

isaiah.feynman · Answer

Polynomial long division now!

ganeshie8 · Answer

yeah thats the only way i see.. factoring is not so obvious here

anonymous · Answer

Doing that, I got 11 as quotient and $24x^3-264x-480$ as remainder.

So we have $\dfrac{11x^4+24x^3+125}{x^4+24x+55} \Longrightarrow11 + \dfrac{24x^3-264x-480}{x^4+24x+55}\~\~\=11 + 24\cdot\dfrac{x^3-11x-20}{x^4+24x+55}$

Numerator looks like something I can factor easily, but I am still stuck... Now what?