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Chapter 2: Problem 71
Solve the inequality. (Round your answers to two decimal places.) $$\frac{1}{2.3 x-5.2}>3.4$$
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Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{3}-x+6$$
Geometry You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters, by cutting equal squares from the corners and turning up the sides. (a) Let \(x\) represent the side length of each of the squares removed. Draw a diagram showing the squares removed from the original piece of material and the resulting dimensions of the open box. (b) Use the diagram to write the volume \(V\) of the box as a function of \(x .\) Determine the domain of the function. (c) Sketch the graph of the function and approximate the dimensions of the box that will yield a maximum volume. (d) Find values of \(x\) such that \(V=56 .\) Which of these values is a physical impossibility in the construction of the box? Explain.
Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) $$2,5+i$$
Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. $$f(x)=x^{4}+6 x^{2}-27$$
Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{2}-x+56$$
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