How to set a polynomial as a variable

I'm trying to create an m script that will give me different polynomials as results.

I want to know how to set up the code so that

A = x^2+1

but I won't need the value of x and variable A will remain as a polynomial.

A doesn't have to be a single polynomial, it could be an array of polynomials.

I wish to put this in a for loop so it would be nice to know how.

In the end, the code will resemble something like this

for i = 1:100
    syms x
    v1 = x^2+1;
    v2 = x^5+4;
    v3 = x^23-45;
    c1 = i;
    c2 = i^2;
    c3 = i^3;
    A{i} = c1*v1+c2*v2+c3*v3;
end

And of course, there will be no value of x because they are all polynomials.

Please help. Thank you.

Answer 1

[Andrei Bobrov]

B = zeros(24,3);
B(sub2ind(size(B),[22,24,19,24,1,24],[1,1,2,2,3,3])) = [1,1,1,4,1,-45];
ii = bsxfun(@power,reshape(1:100,1,1,[]),1:3);
A = num2cell(squeeze(sum(bsxfun(@times,ii,B),2)),1);