document.write( "Question 1175008: factor the following:\r
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Algebra.Com's Answer #800545 by ikleyn(52797)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Actually, this polynomial can not be factored, because IT HAS NO rational roots.\r\n" );
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document.write( "To prove it, use the Rational root theorem test.\r\n" );
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document.write( "For it, you should test if the divisors of the constant term \"7\" are roots of this polynomial.\r\n" );
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document.write( "In other words, you should check if some of the four integer numbers  -1, 1, -7, 7 is the root of the polynomial.\r\n" );
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document.write( "It is easy to check - I did it using MS Excel spreadsheet in my computer.\r\n" );
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document.write( "The answer is \"NO\" : no one of these integer numbers is the root of the polynomial.\r\n" );
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document.write( "It means that the polynomial HAS NO rational roots,\r\n" );
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document.write( "and hence, CAN NOT be factorable over integer numbers.\r\n" );
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\n" ); document.write( "\n" ); document.write( "What I said above,  proves that the given polynomial has no linear factors over rational numbers.\r
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\n" ); document.write( "\n" ); document.write( "But a potential opportunity still remains to factor it into the product of quadratic polynomials.\r
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\n" ); document.write( "\n" ); document.write( "In the Internet,  there are several sites offering free of charge solvers to factor polynomials.\r
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\n" ); document.write( "\n" ); document.write( "I will not refer to concrete sites/solvers --- you can easily find them on your own  IF  YOU  WISH.\r
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\n" ); document.write( "\n" ); document.write( "I tried some of them  (three or four) --- they all said that factoring is impossible over rational numbers.\r
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\n" ); document.write( "\n" ); document.write( "One site was even more talkative:  it even gave me the roots,  that were irrational numbers.\r
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\n" ); document.write( "\n" ); document.write( "It is the solver\r
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\n" ); document.write( "\n" ); document.write( "https://www.wolframalpha.com/input/?i=x%5E4-8x%5E3%2B22x%5E2-24x%2B7\r
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\n" ); document.write( "\n" ); document.write( "But its conclusion about potential factorability into the product of quadratic polynomial
\n" ); document.write( "with rational (or integer) coefficients was  NEGATIVE,  too :   I M P O S S I B L E . \r
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