Find the quotient of the given polynomial division: $\left(4 x^{4}+5\right) \div\left(x^{2}+1\right)$

Step 1 ：Define the polynomials to be divided: \(p1 = 4x^4 + 5\) and \(p2 = x^2 + 1\)

Step 2 ：Perform the polynomial division to find the quotient. The remainder is not needed in this case, as the question only asks for the quotient.

Step 3 ：The quotient of the given polynomial division is \(\boxed{4x^2}\)