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Chapter 2: Problem 97
Find the value of \(k\) such that \(x-4\) is a factor of \(x^{3}-k x^{2}+2 k x-8.\)
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The pH of a solution decreases by one unit. By what factor does the hydrogen ion concentration increase?
Simplify the rational expression by using long division or synthetic division. \(\frac{x^{4}+6 x^{3}+11 x^{2}+6 x}{x^{2}+3 x+2}\)
Sketching Graphs of Quadratic Functions In }} \\ {\text { Exercises } 13-16, \text { sketch the graph of each quadratic }} \\ {\text { function and compare it with the graph of } y=x^{2} .}\end{array} $$ \begin{array}{ll}{\text { (a) } f(x)=(x-1)^{2}} & {\text { (b) } g(x)=(3 x)^{2}+1} \\ {\text { (c) } h(x)=\left(\frac{1}{3} x\right)^{2}-3} & {\text { (d) } k(x)=(x+3)^{2}}\end{array} $$
Complex Solutions of a Quadratic Equation. Use the Quadratic Formula to solve the quadratic equation $$4.5 x^{2}-3 x+12=0$$
Finding Quadratic Functions In Exercises \(65-70\) , find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given \(x\) -intercepts. (There are many correct answers.) $$ (-1,0),(3,0) $$
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