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Chapter 0: Problem 3
Factor out the greatest common factor. $$3 x^{2}+6 x$$
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Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When checking a radical equation's proposed solution, I can substitute into the original equation or any equation that is part of the solution process.
Explain how to simplify a rational expression.
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. The rational expressions $$\frac{7}{14 x} \text { and } \frac{7}{14+x}$$ can both be simplified by dividing each numerator and each denominator by 7
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