Answer:
f(x) = x^3 - 8x^2 + 9x + 18
Step-by-step explanation:
To write a degree 3 polynomial with zeros 3, 6, and -1, we can use the factor theorem. Since the zeros are 3, 6, and -1, the factors of the polynomial would be (x - 3), (x - 6), and (x + 1).
To find the polynomial, we multiply these factors together:
(x - 3)(x - 6)(x + 1)
Expanding this expression gives us the polynomial in standard form:
(x - 3)(x - 6)(x + 1)
= (x^2 - 6x - 3x + 18)(x + 1)
= (x^2 - 9x + 18)(x + 1)
= x^3 + x^2 - 9x^2 - 9x + 18x + 18
= x^3 - 8x^2 + 9x + 18
As an answer, the degree 3 polynomial with zeros 3, 6, and -1 is:
f(x) = x^3 - 8x^2 + 9x + 18
