17-1: **Explain why a polynomial of degree 3 has at least one root.**Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3?- **A.** If \( f(x) \) has a leading term of \( ax^3 \), then either \(\lim_{x \to \infty} f(x) = \infty\) and \(\lim_{x \to -\infty} f(x) = -\infty\) when \( a > 0 \), or \(\lim_{x \to \infty} f(x) = -\infty\) and \(\lim_{x \to -\infty} f(x) = \infty\) when \( a < 0 \).- **B.** If \( f(x) \) has a leading term of \( ax^3 \), then either \(\lim_{x \to \infty} f(x) = \infty\) and \(\lim_{x \to \infty} f(x) = -\infty\) when \( a > 0 \), or \(\lim_{x \to \infty} f(x) = -\infty\) and \(\lim_{x \to \infty} f(x) = \infty\) when \( a < 0 \).- **C.** If \( f(x) \) has a leading term of \( ax^3 \), then \(\lim_{x \to \infty} f(x) = \lim_{x \to -\infty} f(x) = b\) for some real number \( b \).

Name: 17-1: **Explain why a polynomial of degree 3 has at least one root.**S
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 17-1: **Explain why a polynomial of degree 3 has at least one root.**Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3?- **A.** If \( f(x) \) has a leadin