Let f(x)and g(y) be two monic polynomials of degree=n having complex coefficients.
We know that there exist complex numbers ai,bi,ci∀1≤i≤n, such that
f(x)\minus{}g(y)\equal{}\prod_{i\equal{}1}^n{(a_ix\plus{}b_iy\plus{}c_i)}.
Prove that there exists a,b,c∈C such that
f(x)\equal{}(x\plus{}a)^n\plus{}c\text{ and }g(y)\equal{}(y\plus{}b)^n\plus{}c. algebrapolynomialcomplex numbersalgebra proposed