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 $f$ ?

Answer

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Answer

$\boxed{3}$ is the degree of $f(x)$

Steps

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 $f(x)$