Find the complex zeros of the following polynomial function. Write $f$ in factored form.
$f (x) = x^{3} - 8 x^{2} + 25 x - 26$

Answer

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Answer

The complex zeros of the polynomial function $f (x) = x^{3} - 8 x^{2} + 25 x - 26$ are $2$ , $3 - 2 i$ , and $3 + 2 i$ .

Steps

Step 1 ：Set the function equal to zero and solve for x to find the real zeros of the polynomial function.

Step 2 ：The real zeros of the polynomial are 2, 3 - 2i, and 3 + 2i.

Step 3 ：Since these zeros are already complex, there is no need to perform synthetic division and solve a quadratic equation.

Step 4 ：Therefore, the complex zeros of the polynomial are 2, 3 - 2i, and 3 + 2i.

Step 5 ：The complex zeros of the polynomial function $f (x) = x^{3} - 8 x^{2} + 25 x - 26$ are $2$ , $3 - 2 i$ , and $3 + 2 i$ .