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Chapter 0: Problem 6
Find the degree of the polynomial. $$-4 x^{3}+7 x^{2}-11$$
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Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).
Find \(b\) such that \(\frac{7 x+4}{b}+13=x\) will have a solution set given by \(\\{-6\\}\).
Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.
a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.
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