Question

(c) $h(x) = -5x^2(3x + 2)(x - 5)$

• falls to the left and rises to the right
• rises to the left and falls to the right
• rises to the left and rises to the right
• falls to the left and falls to the right

Explanation:

Step1: Find degree of polynomial

First, expand the leading terms: $-5x^2 \cdot 3x \cdot x = -15x^{2+1+1} = -15x^4$. The degree is 4 (even).

Step2: Identify leading coefficient

The leading coefficient is $-15$ (negative).

Step3: Determine end behavior

For even degree polynomials with negative leading coefficients: as $x\to+\infty$, $h(x)\to-\infty$ (falls right); as $x\to-\infty$, $h(x)\to-\infty$ (falls left).

Answer:

Falls to the left and falls to the right