The function H(x) = 3x⁴ + 2x — 5/x + 9x³ – 7 is not a polynomial function

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non–negative integer powers or only positive integer exponents of a variable.

A polynomial with an exponent of 1 is, for instance, 2x+5.

The given polynomial in standard form is written as

H(x) = 3x⁴ + 2x — 5/x + 9x³ – 7

H(x) = 3x⁴ + 9x³ + 2x  – 7 – 5x⁻¹

this shows that on of the term has a negative exponent 5x⁻¹ and hence not a polynomial

the leading coefficient is 3

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