A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, infinite).
The graph of the function is positive on (-infinite, –7).
The graph of the function is negative on (–7, –1).

A mathematical expression having variables and coefficients is referred to as a polynomial expression. The phrase for them is "unknowns."

The root of the polynomial is given below.

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1.

The factor of the polynomial will be

(x + 7)², (x + 1), (x – 2)⁴, and (x – 4)

Then the polynomial with a positive leading coefficient (a) will be

P(x) = a(x + 7)²(x + 1)(x – 2)⁴(x – 4)

Let x = -8, The value of the polynomial will be

P(-8) = a(-8 + 7)²(-8 + 1)(-8 – 2)⁴(-8– 4)

P(-8) = a(-1)²(-7)(-10)⁴(-12)

P(-8) = 551124 a

Then the correct option is C.

More about the polynomial link is given below.

https://brainly.com/question/17822016

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