Algebra and Trigonometry

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Find all real zeros of the polynomial and determine the multiplicity of each.

Find the standard form of the quadratic function shown below:

Find all the rational zeros of the function .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

Use synthetic division to divide.

Find all the real zeros of .

Graph the given function.

Find all real zeros of the polynomial and determine the multiplicity of each.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

An open box is to be made from a square piece of cardboard, 35 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of x, that represents the volume of the box.

Use long division to divide.

Using a graphing utility, graph and approximate the zeros and their multiplicity.

Write in the form when .

Find all the real zeros of .

A farmer has 240 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.

If is a root of , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Determine the vertex of the graph of the quadratic function .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .