Rational polynomial

Algebra Level 4

f(x)f(x) and g(x)g(x) are monic polynomials with integer coefficients such that

f(x)g(x)=x3+8x52x4+4x3\frac{f(x)}{g(x)} =\frac{x^3+8}{x^5-2x^4+4x^3}

and gcd(f(x),g(x))=1 \gcd(f(x), g(x) ) = 1 . What is the value of f(4)+g(4) f(4) + g(4) ?

Details and assumptions

You may use the fact that f(4)g(4)=332 \frac{ f(4) } { g(4) } = \frac{3}{32} .

×

Problem Loading...

Note Loading...

Set Loading...