Final answer:
To write a polynomial with given zeros of -2, 5, and -6, you create factors (x + 2), (x - 5), and (x + 6), expand them by multiplying, and combine like terms to obtain the polynomial x^3 + 3x^2 - 28x - 60.
Step-by-step explanation:
To write a polynomial with the given zeros of -2, 5, and -6, we can construct the polynomial by finding the factors associated with each zero and then expanding them. Since a zero of a polynomial is the value of x that makes the function equal to zero, each factor can be represented as x - (zero). Therefore, the factors for the given zeros are (x + 2), (x - 5), and (x + 6).
The polynomial in factored form is: (x + 2)(x - 5)(x + 6). To fully expand this and write it in standard form, we need to multiply each of these factors:
- Multiply (x + 2) and (x - 5) first:
- This gives us x2 - 3x - 10.
- Next, multiply this result by (x + 6):
- This expands to x3 + 6x2 - 3x2 - 18x - 10x - 60.
- Combine like terms to obtain the fully expanded polynomial in standard form:
- Your answer is x3 + 3x2 - 28x - 60.