1. The problem asks to verify the correctness of the answers given for the polynomial function $h(x) = 2(x - 1)^3 (x + 4)^2$. 2. First, check the degree and leading coefficient. - Degree is the sum of the exponents: $3 + 2 = 5$. - Leading coefficient is the coefficient of the highest degree term, which is $2$. These match the given answers: Degree 5, Leading Coefficient 2. 3. Next, check the y-intercept by evaluating $h(0)$: $$h(0) = 2(0 - 1)^3 (0 + 4)^2 = 2(-1)^3 (4)^2 = 2(-1)(16) = -32$$ The y-intercept is $(0, -32)$, which matches the given answer. 4. Check the x-intercepts and multiplicities: - From the factors, zeros are at $x=1$ with multiplicity 3 and $x=-4$ with multiplicity 2. The user wrote $x = -1$ and $4$, which is incorrect. The correct zeros are $x=1$ and $x=-4$. 5. Behavior at zeros: - Odd multiplicity (3) at $x=1$ means the graph crosses the x-axis. - Even multiplicity (2) at $x=-4$ means the graph bounces off the x-axis. The user wrote "1 through" and "4 bounce" but with wrong zeros. 6. End behavior: - Since degree is odd (5) and leading coefficient positive (2), as $x \to -\infty$, $h(x) \to -\infty$ (down left), and as $x \to \infty$, $h(x) \to \infty$ (up right). This matches the description. 7. Conclusion: Degree, leading coefficient, y-intercept, and end behavior are correct. However, the x-intercepts and multiplicities are incorrect in the user's answer. Therefore, not all answers are correct.