As I'v learned about polynomials, I run into this quadrinomial:
$$x^3+300x^2+30000x-953125 = 0$$
I've been studied how to factor this quadrinomial but didn't quite understand how it's done, here is how I've studied(I probably didn't get the following steps wrong):
I should ask myself how big
x has to be for the linear term and the constant to add to
Divide the constant by the coefficient of the linear term, its around
30, now how would I know if
30 is a reasonable approximation for
I should check the result when
x = 30 for the quadratic and cubic terms and if each of them is smaller than the constant then it's a reasonable approximation.
As I checked with other polynomials dividing the constant with the linear term always produce a number that is pretty close to the
I know I'm probably misunderstood most of the things, but if anyone can help me figure out why and how I will be very thankful.
I'm sorry for not being clear about my question, I try to understand why after dividing the constant by the linear and getting something around
30, why It's considered as reasonable approximation for the factor when both of the following came up true: $$30^3 < 30*30,000$$ and $$300*30^2 < 30*30,000$$ It's something I've learned and couldn't understand why it's true to do so.