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Exercises Polynomials and factoring

Example 4 from Algebra and Trigonometry, 5.2 Power Functions and Polynomial Functions

Identifying Polynomial Functions

Which of the following are polynomial functions?

\begin{matrix} f (x) & = & 2 x^{3} \cdot 3 x + 4 \\ g (x) & = & - x (x^{2} - 4) \\ h (x) & = & 5 \sqrt{x + 2} \end{matrix}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
The first two functions are examples of polynomial functions because they can be written in the form $f (x) = a_{n} x^{n} + ... + a_{2} x^{2} + a_{1} x + a_{0},$ where the powers are non-negative integers and the coefficients are real numbers.
- $f (x)$ can be written as $f (x) = 6 x^{4} + 4.$
- $g (x)$ can be written as $g (x) = - x^{3} + 4 x .$
- $h (x)$ cannot be written in this form and is therefore not a polynomial function.

How did it go?

PreviousIdentifying the End Behavior of a Power Function.Next Identifying the Degree and Leading Coefficient of a Polynomial Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.