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, determine the highest power of $x$:
$h(x) = -5x^2(3x+2)(x-5)$. Multiply the leading terms: $-5x^2 \cdot 3x \cdot x = -15x^{2+1+1} = -15x^4$. Degree = 4 (even).

Step2: Identify leading coefficient

Leading coefficient is $-15$ (negative).

Step3: Apply end behavior rules

For even degree polynomials:

• If leading coefficient < 0: graph falls to left and right.

Answer:

Falls to the left and falls to the right