A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree,which statement about the graph is true?

a. The graph of the function is positive on (-6, -2).
b. The graph of the function is negative on (-∞o, 0).
c. The graph of the function is positive on (-2, 4).
d. The graph of the function is negative on (4, ∞).

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Given:

The root of -6 with multiplicity 1,

The root of -2 with multiplicity 3,

The root of 0 with multiplicity 2,

The root of 4 with multiplicity 3.

To calculate the degree of the polynomial function, Add up the multiplicities;

D = 1 + 3 + 2+ 3

D = 9 - (odd number)

The interval of the first root;

(-∞, -6)

The interval of the second root;

(-6, -2)

If the function has a positive leading coefficient and is of an odd degree then it will start with negative values, until it reaches the smallest root, before it switched to positive values.

means that the function increases at the interval (-6, -2).

Hence, option (a) is correct. The graph of the function is positive on (-6, -2).

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