1. **Problem statement:** Given the function $$y = x^3 + x^2 - 4x - 4$$, answer the following: 2. **End behavior:** To find the end behavior, analyze the leading term of the polynomial, which dominates as $$x \to \pm \infty$$. 3. The leading term is $$x^3$$, so: $$\lim_{x \to -\infty} y = \lim_{x \to -\infty} x^3 = -\infty$$ $$\lim_{x \to \infty} y = \lim_{x \to \infty} x^3 = \infty$$ 4. **Degree and leading coefficient:** The degree of the polynomial is the highest power of $$x$$, which is 3. The leading coefficient is the coefficient of $$x^3$$, which is 1. 5. **Finding zeros knowing $$x=2$$ is a root:** Use polynomial division or synthetic division to divide $$y$$ by $$x-2$$. Synthetic division setup: 2 | 1 1 -4 -4 Carry down 1: Multiply 2*1=2, add to 1: 3 Multiply 2*3=6, add to -4: 2 Multiply 2*2=4, add to -4: 0 (remainder) So quotient is $$x^2 + 3x + 2$$. 6. Factor the quadratic: $$x^2 + 3x + 2 = (x+1)(x+2)$$ 7. Therefore, zeros are $$x=2$$, $$x=-1$$, and $$x=-2$$. **Final answers:** - $$\lim_{x \to -\infty} y = -\infty$$ - $$\lim_{x \to \infty} y = \infty$$ - Degree = 3 - Leading coefficient = 1 - Zeros: $$x=2$$, $$x=-1$$, $$x=-2$$