Using the Intermediate Value Theorem, determine if there exists at least one zero for the polynomial function \( f(x) = x^{3} - 4x + 1 \) in the interval \([-3, 0]\).

An ice cube that is 4 cm on each side is melting at a rate of \( 3 \mathrm{~cm}^{3} \) per minute. How fast is the length of the side decreasing? At the moment when the ice cube is 4 cm on each side, the side length is decreasing at a rate of approximately \( \square \mathrm{cm} \) per minute. (Type an integer or decimal rounded to three decimal places as needed.)

1. \( 16^{2 x-3}=4^{x+2} \)

1. \( \frac{a+2}{a^{2}+2 a+4} \cdot \frac{a^{3}-8}{2 a^{2}-8} \)

Question 8 Solve the equation by completing the square. \( x^{2}+6 x+6=0 \) \( \begin{array}{l}x=-3 \pm \sqrt{3} \\ x=3 \pm 2 \sqrt{3} \\ x=3 \pm \sqrt{3} \\ x=-3 \pm 2 \sqrt{3}\end{array} \)

6) A set of six numbers have a median of 5 . - All of the numbers are even. - The range of the numbers is 6 . Write down a possible set of six numbers.