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- Thread starter Genius271828
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Mark44

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This isn't an equation, so there's nothing to solve. You can simplify it, by eliminating factors that are common to both the numerator and denominator, or you can carry out polynomial long division.How would you go about solving (4(x^3)+38(x^2)+44x-20)/(20+12x+x^2), without the use of a computer

Genius271828 said:, further, what about functions which have more x components, with higher powers. Also what process do computers use to solve these.

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f(x)=(4(x^3)+38(x^2)+44x-20)/(20+12x+x^2), to find when this is equal to 0 (or if it ever does) and what method is used to determine these propertiesThis isn't an equation, so there's nothing to solve. You can simplify it, by eliminating factors that are common to both the numerator and denominator, or you can carry out polynomial long division.

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Mark44

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Look for values of x that make the numerator equal to zero. The best way to do that is to factor the numerator.f(x)=(4(x^3)+38(x^2)+44x-20)/(20+12x+x^2), to find when this is equal to 0 (or if it ever does) and what method is used to determine these properties

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mathwonk

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Thjis is explained in section IV, (see page 253, and 264), of the excellent algebra book of euler:

https://archive.org/details/elementsofalgebr00eule

as well as the more complicated method for solving 4th degree equations. Equations of 5th degree and higher cannot be solved in general by formulas involving only the taking of roots, and can only be approxmated by numerical methods such as newton's method.

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