Algebra.Com's Answer #110551 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
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Please show me how to work out this problem. I know the roots are -1/3, -1/2, and 3, but I don't know how to work the problem by hand to find the answer. Please help so I know how to solve this kind of problem in the future! \r
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document.write( "That's correct. Now observe that all the coefficients\r\n" );
document.write( "can be divided by -4, so we do that:\r\n" );
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document.write( "If there is any rational root, its numerator must divide\r\n" );
document.write( "evenly into the absolute value of the constant term, and \r\n" );
document.write( "its denominator must divide evenly into the absolute value\r\n" );
document.write( "of the coefficient of the leading term (the term with the\r\n" );
document.write( "largest exponent.\r\n" );
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document.write( "So the possible numerators are 1 and 3, for these are the \r\n" );
document.write( "only integers which will divide evenly into 3.\r\n" );
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document.write( "the possible denominators are 1, 2, 3 and 6, for these are the \r\n" );
document.write( "only integers which will divide evenly into 6. \r\n" );
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document.write( "So all possible rational (common fraction) roots are\r\n" );
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document.write( "± , ± , ± , ± , ± , ± , ± , ± .\r\n" );
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document.write( "Which reduce to:\r\n" );
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document.write( "± , ±, ±, ±, ± , ±, ±, ±.\r\n" );
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document.write( "Eliminating the duplicates, all possible rational roots are:\r\n" );
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document.write( "±, ±, ±, ±, ±, ±.\r\n" );
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document.write( "First we try the easiest possible root 1, using synthetic division:\r\n" );
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document.write( " 1| 6 -13 -14 -3 \r\n" );
document.write( " | 6 -7 -21 \r\n" );
document.write( " 6 -7 -21 -24\r\n" );
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document.write( "That doesn't leave a 0 remainder so 1 is not a root.\r\n" );
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document.write( "So we try the next easiest possible root -1, using synthetic division:\r\n" );
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document.write( " -1| 6 -13 -14 -3 \r\n" );
document.write( " | -6 19 -5 \r\n" );
document.write( " 6 -19 5 -8\r\n" );
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document.write( "That doesn't leave a 0 remainder either so -1 is not a root.\r\n" );
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document.write( "So we try the next easiest possible root 3, using synthetic division:\r\n" );
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document.write( " 3| 6 -13 -14 -3 \r\n" );
document.write( " | 18 15 3 \r\n" );
document.write( " 6 5 1 0\r\n" );
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document.write( "That leaves a 0 remainder so 3 is a root. So we have now\r\n" );
document.write( "factored the left side of:\r\n" );
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document.write( "as\r\n" );
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document.write( "Now we factor the second parentheses:\r\n" );
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document.write( "Now we use the zero factor property\r\n" );
document.write( "to set each factor = 0\r\n" );
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document.write( " gives the solution  \r\n" );
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document.write( " gives the solution  \r\n" );
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document.write( " gives the solution  \r\n" );
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document.write( "Edwin
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