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Reed College Department of Mathematics & Statistics

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Worksheet Polynomial and Rational Inequalities

1.

Find the interval on the real number line for which the radicand is nonnegative (greater than or equal to zero) so that the radical
\begin{equation*} \sqrt{4 x + 5} \end{equation*}
defines a real number. Write your answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U. If needed enter \(\infty\) as infinity and \(-\infty\) as -infinity .
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For example, you may write (-infinity, 5] for the interval \((-\infty,5]\) and (-infinity, 5]U(7,9) for \((-\infty,5]\cup(7,9)\text{.}\)
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Your answer:
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Answer.
\(\left[-1.25,\infty \right)\)
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6.

Solve the following inequality. Write your answer using .
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\begin{equation*} -2 (u - 4)(u + 2)^2(u - 11) \leq 0 \end{equation*}
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Answer.
\(\left(-\infty ,4\right]\cup \left[11,\infty \right)\)
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9.

Solve \(\displaystyle{ {9x+4} > {-3x^{2}+12x+40} }\text{.}\) Enter the solution in interval notation.
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Answer.
\(\left(-\infty ,-3\right)\cup \left(4,\infty \right)\)
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