## Quiz 3 :

Polynomial and Rational Functions

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

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E

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

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B

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Find the standard form of the quadratic function shown below:

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D

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

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

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

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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.

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

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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.

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

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

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

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