what is the fundamental algebra result that allows you to equate coefficients for 2 polynomials if they have equal values for all values of x?
and how can you replace this expression-
F(x)=A(x-alpha1)(x-alpha2)....)x-alphar)

with F(x)=A(x-alpha1)^m1(x-alpha2)^m2....(x-alphar)^mr, with A=an
mk are integers =1 and are multiplicities of the roots mk being the multiplicity of alphak
thanks very much!

Question

what is the fundamental algebra result that allows you to equate coefficients for 2 polynomials if they have equal values for all values of x?
and how can you replace this expression-
F(x)=A(x-alpha1)(x-alpha2)....)x-alphar)

with F(x)=A(x-alpha1)^m1(x-alpha2)^m2....(x-alphar)^mr, with A=an
mk are integers >=1 and are multiplicities of the roots mk being the multiplicity of alphak
thanks very much!

anonymous · Answer

$$F(x)=A(x-\alpha1)^m1(x-\alpha2)^m2...$$
$$F(x)=A(x-\alpha1)(x-\alpha2)...(x-\alpha r)$$

anonymous · Answer

how is the condition f(alphak)=0 for k=1,2,r met by replacing these 2 conditions?