Final answer:
To find the real zeros of the polynomial P(x) = x^3 + 8x^2 + 10x - 4, we can use the Rational Root Theorem to find potential rational roots. By testing the possible roots, we find that x = -1 is a solution. Dividing the polynomial by x + 1, we obtain a quadratic equation that can be solved using the quadratic formula to find the remaining solutions.
Step-by-step explanation:
The given polynomial is P(x) = x^3 + 8x^2 + 10x - 4.
To find the real zeros of the polynomial, we can use the Rational Root Theorem to identify potential rational roots. The possible rational roots for P(x) are ±1, ±2, ±4. By testing these values, we find that x = -1 is a solution.
To find the remaining solutions, we can divide P(x) by x + 1 using synthetic division. Performing the division, we get a quadratic equation x^2 + 7x + 3. Using the quadratic formula, we find two more solutions: x ≈ -7.76 and x ≈ -0.24.