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Exercises 107–109 will help you prepare for the material covered in the next section. Factor: x^3+3x^2−x−3
4. Polynomial Functions
Understanding Polynomial Functions
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Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.
A
Polynomial with
B
Polynomial with
C
Polynomial with
D
Not a polynomial function.
Verified step by step guidance1
Identify the given function: \( f(x) = 4x^3 + \frac{1}{2}x^{-1} - 2x + 1 \).
Recall the definition of a polynomial function: A polynomial function is an expression consisting of variables and coefficients, involving only non-negative integer powers of the variable.
Examine each term in the function: \( 4x^3 \), \( \frac{1}{2}x^{-1} \), \( -2x \), and \( 1 \).
Notice that the term \( \frac{1}{2}x^{-1} \) involves a negative exponent, which violates the condition for a polynomial function.
Conclude that since the function contains a term with a negative exponent, it is not a polynomial function.
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