# [Answer] A polynomial function has a root of -5 with multiplicity 3 a root of 1 with multiplicity 2 and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree which statement about the graph is true?

###### Answer: The graph of the function is negative on (3 mc024-3.jpg).
A polynomial function has a root of -5 with multiplicity 3 a root of 1 with multiplicity 2 and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree which statement about the graph is true?

In mathematics a polynomial is an expression consisting of variables (also called indeterminates) and coefficients that involves only the operations of addition subtraction multiplication and non- negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x 2 − 4x + 7 .An example in three variables is x 3 + 2xyz 2 − yz + 1 .

The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root .This includes polynomials with real coefficients since every real number is a complex number with its imaginary part equal to zero.. Equivalently (by definition) the theorem states that the field of complex numbers is algebraically closed.

The (formal) derivative of the polynomial + + ⋯ + is the polynomial + + ⋯ + −. In the case of polynomials with real or complex coefficients this is the standard derivative.The above formula defines the derivative of a polynomial even if the coefficients belong to a ring on which no notion of limit is defined. The derivative makes the polynomial ring a differential algebra.

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Fundamental theorem of algebra – Wikipedia

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Polynomial – Wikipedia

In mathematics an irreducible polynomial is roughly speaking a polynomial that cannot be factored into the product of two non-constant polynomials.The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors that is the field or ring to which the coefficients of the polynomial and its possible factors are supposed to belong.

Using Leibniz’ rule for the determinant the left-hand side of Equation is a polynomial functi…