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

Answer

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Answer

$f (x) = x^{3} + 4 x^{2} - 7 x - 10$

Steps

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: $x^{3} + 4 x^{2} - 7 x - 10$

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