Find the product of following: \( \begin{array}{ll}\text { (a) }\left(x^{3}-4 x+8\right)(3 x+4) & \text { (b) }\left(-x^{2}-3 x+9\right)(-4 x-7) \\ \text { (c) }\left(9 x^{2}-x+15\right)\left(x^{3}-5\right) & \text { (d) }\left(x^{2}-2 x y-y^{2}\right)(x+y)\end{array} \)

2. Expand and simplify \( \begin{array}{ll}\text { a. } 2(x+3) & \text { b. } \quad x\left(x^{2}-3 x\right) \\ \text { c. } \quad(x+7)(x-5) & \text { d. } \quad(x-3)^{2}\end{array} \)

Given the quadratic \( y=-2(x+1)^{2}-7 \) write the equation in standard form.

VERTICAL A. \( 3 X+2=32 \)

Solve for the variable specified. \( A=\pi\left(k^{2}+R^{2}\right) p ; \) for \( k \)

The number of incarcerated adults N (measured in thousands) in a certain country can be approximated by the equation \( \mathrm{N}=-2.8 \mathrm{x}^{2}+72.4 \mathrm{x}+1914 \), where x is the number of years since 2000. In 2012 , the number of incarcerated adults peaked. How many adults were incarcerated in that year? There were \( \square \) incarcerated adults in 2012.