Question

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?
The graph of the function is positive on (-6, -2).
OThe graph of the function is negative on (-co. 0).
The graph of the function is positive on (-2, 4).
OThe graph of the function is negative on (4, co).

Answer 1

The statement that is true about the polynomial is:

Option A: The graph of the function is positive on (-6, -2).

How to interpret the polynomial properties?

The given parameters of the polynomial are:

Root = -6, Multiplicity = 1

Root = -2, Multiplicity = 3

Root = 0, Multiplicity = 2

Root = 4, Multiplicity = 3

Add up the multiplicities, to calculate the degree of the polynomial function:

Degree = 1 + 3 + 2 + 3 = 9 --- odd number

The interval of the first root is:

(-∞, -6)

The interval of the second root is:

(-6, -2)

A polynomial function with an odd degree, and a positive leading coefficient will start with negative values, until it reaches the smallest root, before it switched to positive values.

This means that, the function increases at: (-6, -2)

Hence, option (a) is correct.