Question

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

Answer 1

Answer:

According to the given information, the polymomial expression should have the following factors.

Root of -6 and multiplicity of 1: $(x+6)$

Root of -2 and multiplicity of 3: $(x+2)^{3}$

Root of 0 with a multiplicity of 2: $x^{2}$

Root of 4 and multiplicity of 3: $(x-4)^{3}$

If we sum exponents, we can know the grade of the polnomial:

1 + 3 + 2 + 3 = 9

So, the grade of the polynomial function is 9, which makes it an odd function.

Additionally, the function is

$f(x)=(x+6)x^{2}(x+2)^{3}(x-4)^{3}$

Its graph is attached.