Consider the polynomial function \(p\) given by \(p(x)=5x^3+8x^2-3x+1\). Evaluate the function at \(x=\text-2\).

An open-top box is formed by cutting identical squares out of the corners of a rectangular piece of paper and then folding up the sides. The volume \(V(x)\) in cubic inches of this type of open-top box is a function of the side length \(x\), in inches, of the square cutouts and can be given by \(V(x)=(7-2x)(5-2x)(x)\). What are the dimensions of the rectangular piece of paper?

A rectangular playground space is to be fenced in using the wall of a daycare building for one side and 200 meters of fencing for the other three sides. The area \(A(x)\), in square meters, of the playground space is a function of the length \(x\), in meters, of each of the sides perpendicular to the wall of the daycare building.

1. What is the area of the playground when \(x=50\)?
2. Write an expression for \(A(x)\).
3. What is a reasonable domain for \(A\) in this context?

Tyler finds an expression for \(V(x) \) that gives the volume of an open-top box in cubic inches in terms of the length \(x\), in inches, of the square cutouts used to make it. This is the graph Tyler gets if he allows \(x\) to take on any value between -1 and 7.

Coordinate plane, x, negative 1 to 6 by 1, y, negative 40 to 60 by 10. Curve starts near negative point 5 comma negative 40, increases to approximately 1 point 5 comma 52, decreases through 3 point 5 comma 0 to 5 comma negative 30, then increases through 6 comma 0 to 7 comma 65.

1. What would be a more appropriate domain for Tyler to use instead?
2. What is the approximate maximum volume for his box?

Consider the expression \((3+x)(7-x)\).

1. Is the expression equivalent to \(x^2+4x+21\)? Explain your reasoning.
2. Is the expression \(21+4x+x^2\) in standard form? Explain your reasoning.