1. Given that $x=-1$ is a zero of the polynomial $P(x) = x^3 - 4x^2 + x + 6$, what is the largest remaining zero of $P(x)$? The answer is ___.
2. The polynomial $P(x) = x^3 - 3x^2 - 6x + 8$ has a known zero at $x=4$. When $P(x)$ is divided by $(x-4)$, what is the resulting quotient polynomial $Q(x)$?
3. One zero of the polynomial $P(x) = 2x^3 - 3x^2 - 11x + 6$ is $x=3$. The sum of the other two zeros is ___.
4. A polynomial $P(x)$ of degree 4 has a known zero at $x=2$. If synthetic division is used to divide $P(x)$ by $(x-2)$, what is the degree of the resulting quotient polynomial $Q(x)$?
5. The polynomial $P(x) = x^4 - x^3 - 7x^2 + x + 6$ has a known zero at $x=-2$. The smallest of the remaining zeros is ___.
6. Use the discriminant to determine the nature of the solutions for $4x^2 + 23x - 19 = 0$.
7. If one solution of a quadratic equation with rational coefficients is $2 + \sqrt{5}$, what is the other solution? The other solution is ___.
8. Use the discriminant to determine the nature of the solutions for $3x^2 - 17x + 26 = 0$.
9. Calculate the discriminant of the quadratic equation $2x^2 - 7x + 5 = 0$. The discriminant is ___.
10. How many real solutions does the equation $x^2 + 4x + 4 = 0$ have?