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document.write( "Hi, there-\r\n" );
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document.write( "The Problem: \r\n" );
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document.write( "A Solution:\r\n" );
document.write( "I take it that you want to simplify this expression as much as possible. It's usually the case in math\r\n" );
document.write( "textbooks, that problems like these can be factored. As it turns out, all four of these trinomials are\r\n" );
document.write( "factorable. \r\n" );
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document.write( "We'll start with 6x^2 - 5x - 4. The first term, 6x^2, has factors 6x and x or 2x and 3x. The last term,\r\n" );
document.write( "-4 has factors, 4 and -1, -4 and 1, or -2 and 2. We are looking for a combination of these factors with\r\n" );
document.write( "a sum of the middle term, -5x. We see that 2x, 3x, 1, and -4 work because \r\n" );
document.write( "(3x)(1) + (2x)(-4) = 3x + -8x = -5x.\r\n" );
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document.write( "So, \r\n" );
document.write( "6x^2 - 5x - 4 = ( 2x + 1 )( 3x - 4 )\r\n" );
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document.write( "Using a similar procedure, we find that\r\n" );
document.write( "6x^2 + 5x + 1 = ( 2x + 1 )( 3x + 1 )\r\n" );
document.write( "3x^2 + 7x + 2 = ( 3x + 1 )( x + 2 )\r\n" );
document.write( "3x^2 - 10x + 8 = ( x - 2 )( 3x - 4 )\r\n" );
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document.write( "Therefore,\r\n" );
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\r\n" );
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document.write( "Notice that the factors (2x+1), (3x-4), and (3x+1) are repeated in the numerator and the denominator.\r\n" );
document.write( "There will \"cancel out\" because a number divided by itself equals one (2x+1)/(2x+1)=1, etc.) and\r\n" );
document.write( "multiplying by one does not change the value of an expression.\r\n" );
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document.write( "Thus \r\n" );
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document.write( "Here is a link to a polynomial calculator for finding factors. It includes good explanations:\r\n" );
document.write( "http://www.mathportal.org/calculators/polynomials-solvers/polynomial-factoring-calculator.php\r\n" );
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document.write( "If you find that you are confused about factoring with variables in general, here is a link to an\r\n" );
document.write( "excellent tutorial:\r\n" );
document.write( "http://www.purplemath.com/modules/simpfact.htm\r\n" );
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document.write( "Feel free to email if you have any questions about this solution.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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