https://wiki.math.ucr.edu/index.php?action=history&feed=atom&title=Polynomial_and_Rational_Inequalities 2026-04-22T20:34:55Z Revision history for this page on the wiki MediaWiki 1.35.0 https://wiki.math.ucr.edu/index.php?title=Polynomial_and_Rational_Inequalities&diff=1119&oldid=prev 2015-10-21T03:16:11Z

<p>Created page with &quot;&lt;div class=&quot;noautonum&quot;&gt;__TOC__&lt;/div&gt; ==Introduction== The methods for solving polynomial and rational inequalities are very similar. The main difference is that we have to be...&quot;</p> <p><b>New page</b></p><div>&lt;div class=&quot;noautonum&quot;&gt;__TOC__&lt;/div&gt;<br /> ==Introduction==<br /> <br /> The methods for solving polynomial and rational inequalities are very similar.<br /> The main difference is that we have to be aware of vertical asymptotes when considering rational inequalities.<br /> <br /> ==Polynomial Inequalities==<br /> <br /> Step 1: Put all nonzero terms on the same side, preferably which ever side leads to a positive leading coefficient.<br /> <br /> Step 2: Factor the polynomial as far as possible<br /> <br /> Step 3: Find the zeros of the polynomial<br /> <br /> Step 4: Use the zeros to divide the real number line into regions.<br /> <br /> Step 5: Determine over which regions the polynomial is positive and which regions the polynomial is negative<br /> <br /> Step 6: Write the desired intervals based on the inequality.<br /> <br /> <br /> ==Rational Inequalities==<br /> <br /> The main difference here is during step 3 you want to find the zeros of both numerator and denominator.<br /> Then when you divide the real number line you want to account for the vertical asymptotes and zeros of the function.<br /> <br /> [[Math_5|'''Return to Topics Page]]</div>

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