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Chapter 0: Problem 65
Factor completely, or state that the polynomial is prime. $$3 x^{3}-3 x$$
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List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\\{-7,-0 . \overline{6}, 0, \sqrt{49}, \sqrt{50}\\}$$
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-4(x-y), \text { for } x=8 \text { and } y=3$$
Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \% .\) Now the sale price is reduced by another \(30 \%\). If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$4^{-2}<4^{-3}$$
$$\text { Factor completely.}$$ $$10 x^{2}(x+1)-7 x(x+1)-6(x+1)$$
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