document.write( "Question 1074198: Can someone help me with this?
\n" ); document.write( "Solve the inequality algebraically: x^3-x^2-11x+3/2x^3-7x^2-19x+60 ≥ 0
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Algebra.Com's Answer #688914 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Can someone help me with this?
\n" ); document.write( "Solve the inequality algebraically: x^3-x^2-11x+3/2x^3-7x^2-19x+60 ≥ 0
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\n" ); document.write( "\n" ); document.write( "I can help you under one CERTAIN condition: you will work together with me.\r
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\n" ); document.write( "\n" ); document.write( "Below I prepared the plots for the numerator and denominator polynomials.\r
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document.write( "Plot y = \"x%5E3-x%5E2-11x%2B3\" (red) and y = \"2x%5E3-7x%5E2-19x%2B60\" (green)\r\n" );
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document.write( "1.  The plots clearly say that the numerator has the root -3 and two other real roots that are not integer numbers.\r\n" );
document.write( "    You divide the numerator by (x+3) (long division) and find the quotient polynomial which is quadratic.\r\n" );
document.write( "    Then find the two roots of this quadratic. In this way you will find all the roots of the numerator.\r\n" );
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document.write( "2.  The plots say that the denominator has the roots -3, 4  and one other real root which is not integer number.\r\n" );
document.write( "    You divide the denominator by (x+3)*(x-4) (long division) and find the quotient polynomial which is linear binomial.\r\n" );
document.write( "    This linear binomial will give you the third root of the denominator. In this way you will find all the roots of the denominator.\r\n" );
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document.write( "3.  In the given rational function, write the numerator and denominator as the product of linear factors.\r\n" );
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document.write( "4.  The factor (x+3) will be common for the numerator and denominator.\r\n" );
document.write( "    You can cancel this factor. It doesn't make influence on the solution set you are working on.\r\n" );
document.write( "    As \"anamnesis\", this canceling will remain the hole x = -3 in the solution set.\r\n" );
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document.write( "5.  After canceling, the numerator and denominator will have two factors each.\r\n" );
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document.write( "6.  What to do next ? How to analyse this new rational function ?\r\n" );
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document.write( "    Read about it in the lesson\r\n" );
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document.write( "    - Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials \r\n" );
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document.write( "    in this site.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Yes, it requires some work from your side.\r
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\n" ); document.write( "\n" ); document.write( "But when (and if) you complete it, you will master this subject.\r
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\n" ); document.write( "\n" ); document.write( "It will be your reward.\r
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\n" ); document.write( "\n" ); document.write( "        H a p p y     l e a r n i n g  !\r
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