问题 Suppose that $f$ is a polynomial such that \[ (x-1) \cdot f(x)=3 x^{4}+x^{3}-25 x^{2}+38 x-17 \] What is the degree of $f$ ?

Step 1 ：Given the equation: \((x-1) cdot f(x)=3 x^{4}+x^{3}-25 x^{2}+38 x-17\)

Step 2 ：The degree of the right side of the equation is 4, as the highest power of x is \(x^4\)

Step 3 ：Since \((x-1)\) has a degree of 1, we can subtract 1 from the degree of the right side to find the degree of \(f(x)\)

Step 4 ：degree_f_x = 4 - 1

Step 5 ：\(\boxed{3}\) is the degree of \(f(x)\)