document.write( "Question 1051568: Factor the polynomial:\r
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Algebra.Com's Answer #667037 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Factor the polynomial:\r\n" );
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document.write( "3x²-y²+z²-2xy-4xz\r\n" );
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document.write( "We try for a factorization of\r\n" );
document.write( "the form (Ax+By+Cz)(Dx+Ey+Fz)\r\n" );
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document.write( "We observe:\r\n" );
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document.write( "3x² can only be factored \r\n" );
document.write( "feasibly as 3x and x, so if \r\n" );
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document.write( "3x²-y²+z²-2xy-4xz \r\n" );
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document.write( "factors at all, it would \r\n" );
document.write( "have to factor this way:\r\n" );
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document.write( "(3x_y_z)(x_y_z)\r\n" );
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document.write( "with the proper signs in the blanks:\r\n" );
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document.write( "The term -y² can only be factored \r\n" );
document.write( "feasibly as y and -y.\r\n" );
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document.write( "The term z² can only be factored \r\n" );
document.write( "feasibly either as either \r\n" );
document.write( "z and z, or -z and -z.\r\n" );
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document.write( "The terms in xy will be _3xy_xy,\r\n" );
document.write( "and since that must have sum -2xy,\r\n" );
document.write( "it can only be -3xy+xy, so we know \r\n" );
document.write( "that the factorization thus far\r\n" );
document.write( "must be:\r\n" );
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document.write( "(3x+y_z)(x-y_z)\r\n" );
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document.write( "The terms in xz will be _3xz_xz,\r\n" );
document.write( "and since that sum must be -4xz,\r\n" );
document.write( "it must be -3xz-xz, so we know that\r\n" );
document.write( "the factorization must be\r\n" );
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document.write( "(3x+y-z)(x-y-z)\r\n" );
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document.write( "This will be correct if it turns out\r\n" );
document.write( "that the yz terms cancel out since\r\n" );
document.write( "there are no yz terms in the original\r\n" );
document.write( "polynomial.  And it does turn out that\r\n" );
document.write( "the terms in yz are -yz+yz and they\r\n" );
document.write( "do cancel out.\r\n" );
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document.write( "So the factorization is\r\n" );
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document.write( "(3x+y-z)(x-y-z)\r\n" );
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document.write( "Edwin
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