Question

Is there anyone who can help me with this problem... (advanced algebra)
(x^2-25)/x^5+x^4+18x^3+18x^2-175x-175
I'm trying to find the zeros. I have to do this first... Any help?

Answer 1

Hint: if P/Q = 0, then

P/Q = 0

P = 0*Q

P = 0

So if P/Q = 0, then P = 0

The value of Q, it turns out, is completely irrelevant. As long as Q is not zero, then everything should be fine.

Answer 2

Um.... I'm sorry but I'm even more confused by that answer.

Answer 3

P and Q can be any number or expression. So in this case P = x^2 - 25 and Q = x^5+x^4+18x^3+18x^2-175x-175


So

(x^2-25)/(x^5+x^4+18x^3+18x^2-175x-175)

becomes

P/Q

Answer 4

ah perhaps I should have mentioned that I am supposed to be solving this by long division and therein lies my problem. I am terrible at long division. Especially with problems like that.

Answer 5

There's no need to use long division though since only the numerator matters.

Answer 6

Basically, if (x^2-25)/(x^5+x^4+18x^3+18x^2-175x-175) = 0, then x^2 - 25 = 0

Answer 7

Does that make sense?

Answer 8

If not, then think of something like this



If (x+1)/(x+2) = 0, then...


(x+1)/(x+2) = 0

x+1 = 0*(x+2) ... multiply both sides by x+2

x+1 = 0x+0*2

x + 1 = 0 + 0

x + 1 = 0


So if (x+1)/(x+2) = 0, then x + 1 = 0


This shows us that the denominator plays no role whatsoever in finding the zeros.

Answer 9

\[x^{2} -25\div x^{5}+x^{4}+18^{3}+18^{2}-175x-175\]
That's not what I'm looking for though. This is just a piece of the big problem I have to solve. What I need to do is solve this equation, and use the answer to find the zeros of the original.

Answer 10

That's the problem. What you just wrote isn't an equation.

Answer 11

Also, I'm assuming that x^5+x^4+18x^3+18x^2-175x-175 is all in the denominator correct?

Answer 12

That is the dividend. the x^2-25 is the divisor. The point is that I have to legitimately divide the equation in order to finish the overall problem.

Answer 13

Oh so it's really something like