Problem

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 $f$ ?

Solution

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 \(f(x)\)

From Solvely APP
Source: https://solvelyapp.com/problems/26130/

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