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Chapter 5: Problem 13
Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{x^{3}-6 x^{2}+7 x-2}{x-1}$$
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Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1
What polynomial, when divided by \(3 x^{2}\), yields the trinomial \(6 x^{6}-9 x^{4}+12 x^{2}\) as a quotient?
In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{8 x^{6} y^{3}-12 x^{8} y^{2}-4 x^{14} y^{6}}{-4 x^{6} y^{2}}$$
Perform the indicated operations. $$(y+6)^{2}-(y-2)^{2}$$
Explain the difference between performing these two operations: $$2 x^{2}+3 x^{2} \text { and }\left(2 x^{2}\right)\left(3 x^{2}\right)$$
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