MATLAB: Transforming from Maclaurin to Taylor

factorizationMATLAB

I have a polynomial function in terms of x, in which the highest power never exceeds 6. This function will look like a Maclaurin Series with finite terms. How to tell Matlab to rewrite this function into a Taylor one, which will express the function in terms of (x-a), where a is a real, positive number?
E.g. Original function: f(x)=x^3+x^2+x+1
Transformed functions:
If a=1, g(x)=(x-1)^3+4*(x-1)^2+6*(x-1)+4
if a=2, g(x)=(x-2)^3+7*(x-2)^2+17*(x-2)+15
and etc.
I tried using rem but it returned an error message, saying that f(x) must be a real value in order to use rem.

Best Answer

If i understand correctly, your code looks something like this:
syms x
f(x) = x^3 + x^2 + x +1
f(x-1)
f(x-2)
And you want to expand the expressions. This can be done with the expand command:
expand(f(x-1))
>> x^3 - 2*x^2 + 2*x
expand(f(x-2))
>> x^3 - 5*x^2 + 9*x - 5
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