What are Polynomial Functions?
A **polynomial function** is a function that can be written in the form: $$P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$$
In this equation:
- The coefficients ($a_n, a_{n-1}, \dots, a_0$) are **real numbers**.
- The exponents ($n, n-1, \dots, 1, 0$) must be **non-negative integers**.
The **degree** of the polynomial is the highest exponent, $n$. The **leading coefficient** is the coefficient of the term with the highest exponent, $a_n$. The **constant term** is $a_0$.
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Video: Graphing & End Behavior!
Watch this video to see how the degree and leading coefficient of a polynomial determine its graph and end behavior. 📈
Practice Problems
Answer the following questions about polynomial functions!
1) What is the degree of the polynomial $P(x) = 3x^4 - 2x^2 + 5x - 1$?
2) What is the leading coefficient of $P(x) = -x^3 + 7x^2$?
3) What is the constant term of $P(x) = 2x^5 + x - 8$?
4) Is $f(x) = \sqrt{x} + 2x - 1$ a polynomial function? (yes/no)
⚡ Polynomial Speed Quiz
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