Problem

Find a polynomial function of degree 3 with real coefficients that has the given zeros. \[ -1,2,-5 \] The polynomial function is $f(x)=x^{3}+\square x^{2}-7 x-10$.

Solution

Step 1 :Given the zeros of the polynomial function: \(-1, 2, -5\)

Step 2 :Find the factors using the zeros: \((x + 1)(x - 2)(x + 5)\)

Step 3 :Multiply the factors to find the polynomial function: \(x^3 + 4x^2 - 7x - 10\)

Step 4 :\(\boxed{f(x) = x^3 + 4x^2 - 7x - 10}\)

From Solvely APP
Source: https://solvelyapp.com/problems/21868/

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