Problem

Given that 2 is a zero of the polynomial function $f(x)$, find the remaining zeros. \[ f(x)=x^{3}-10 x^{2}+36 x-40 \] List the remaining zeros (other than 2). (Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)

Solution

Step 1 :Given that 2 is a zero of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\), we can find the remaining zeros by dividing the polynomial by \((x - 2)\).

Step 2 :The quotient polynomial is then \(x^{2} - 8x + 20\).

Step 3 :We find the zeros of this polynomial by setting it equal to zero and solving for \(x\).

Step 4 :Solving \(x^{2} - 8x + 20 = 0\) gives us the remaining zeros of the original polynomial.

Step 5 :Final Answer: The remaining zeros of the polynomial function \(f(x) = x^{3} - 10x^{2} + 36x - 40\) are \(\boxed{4, 5}\).

From Solvely APP
Source: https://solvelyapp.com/problems/45797/

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