Can someone explain this question?
Let b be a real number. Find the Taylor polynomials for g(x)=x^4+6b^2x^2+b^4 in powers of x + b.

I don't understand what "in powers of x + b" means

Question

Can someone explain this question?
Let b be a real number. Find the Taylor polynomials for g(x)=x^4+6b^2x^2+b^4 in powers of x + b.

I don't understand what "in powers of x + b" means

anonymous · Answer

expand around x = -b rather than simply taking the taylor polynomial at x = 0

anonymous · Answer

you'd like to understand the behavior of g(x) for values of x that are very close to x = -b by writing g(x) = A(x+b)^4 + B(x+b)^3 + C(x+b)^2 + D(x+b) + E; I suppose you could figure out ABCDE by hand but that's what formula for Taylor expansion is for...

anonymous · Answer

attachment

anonymous · Answer

you can simplify the fractions