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Chapter 0: Problem 80
State the name of the property illustrated. $$7 \cdot(11 \cdot 8)=(11 \cdot 8) \cdot 7$$
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$$\text { Factor completely.}$$ $$12 x^{2}(x-1)-4 x(x-1)-5(x-1)$$
$$\text { Factor completely.}$$ $$7 x^{4}+34 x^{2}-5$$
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?
Your computer store is having an incredible sale. The price on one model is reduced by \(40 \% .\) Then the sale price is reduced by another \(40 \% .\) If \(x\) is the computer's original price, the sale price can be modeled by $$(x-0.4 x)-0.4(x-0.4 x)$$ a. Factor out \((x-0.4 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(40 \%\) reduction followed by a \(40 \%\) reduction, is the computer selling at \(20 \%\) of its original price? If not, at what percentage of the original price is it selling?
Using an example, explain how to factor out the greatest common factor of a polynomial.
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