The polynomial h(x) is to be factored into linear terms given -2 is a zero. After dividing by (x + 2), we solve the resulting quadratic to find the other zeros and express h(x) as the product of these linear factors.
The student is asking to express the polynomial h(x) = x³ - 2x² - 11x - 6 as a product of linear factors given that -2 is a zero of h(x). Since -2 is a zero, (x + 2) is one of the factors. To find the remaining factors, we perform polynomial division or synthetic division to divide h(x) by (x + 2), giving us a quadratic equation that we can then factor further or solve using the quadratic formula.
After the division, we obtain the quadratic equation ax² + bx + c, where a, b, and c are real numbers obtained from the division. The roots of this quadratic equation are the other two zeros of the polynomial h(x). By finding these zeros, we can factor h(x) completely.
In conclusion, the final answer will be in the form of h(x) = (x + 2)(x - p)(x - q), where p and q are the zeros obtained from the quadratic equation resulting from the division step. The explanation in 150 words has guided us through the process of finding all linear factors of the polynomial.