Final answer:
The polynomial function of least degree with zeros x = -3, x = √6, and x = -√6 is given by P(x) = (x + 3)(x² - 6) or P(x) = x³ + 3x² - 6x - 18.
Step-by-step explanation:
The question is asking for a polynomial function of least degree with given zeros. To find this polynomial, we can use the zeros x = -3, x = √6, and x = -√6. We know that for a zero at x = a, the factor of the polynomial will be (x - a). Therefore, we can write the polynomial as:
P(x) = (x + 3)(x - √6)(x + √6).
Since (x - √6)(x + √6) is a difference of squares, it simplifies to x² - 6. The polynomial function of least degree that includes all given zeros is then:
P(x) = (x + 3)(x² - 6) = x³ + 3x² - 6x - 18.
This is the required polynomial function.