document.write( "Question 319327: Given that -1 is a zero of the polynomial g(x)=x^3-3x^2-3x+1, express g(x) as a product of linear factors.
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Algebra.Com's Answer #228636 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%22g%28x%29%22=x%5E3-3x%5E2-3x%2B1\"\r\n" );
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document.write( "Move the \"+1\" term:\r\n" );
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document.write( "\"%22g%28x%29%22=x%5E3%2B1-3x%5E2-3x\"\r\n" );
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document.write( "Factor the first two terms, \"x%5E3%2B1\", as \"%28x%2B1%29%28x%5E2-x%2B1%29\"\r\n" );
document.write( "Factor the last two terms, \"-3x%5E2-3x\", as \"-3x%28x%2B1%29\"\r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29%28x%5E2-x%2B1%29-3x%28x%2B1%29\"\r\n" );
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document.write( "Factor out \"%28x%2B1%29\"\r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29\"\"%22%5B%22\"\"%28x%5E2-x%2B1%29-3x\"\"%22%5D%22\"\r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29%28x%5E2-x%2B1-3x%29\"\r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29%28x%5E2-4x%2B1%29\"\r\n" );
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document.write( "Now we have to find the two zeros of \"x%5E2-4x%2B1\"\r\n" );
document.write( "which is not factorable with integers.  So we use the \r\n" );
document.write( "quadratic formula:\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r\n" );
document.write( "\"x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A%281%29%2A%281%29+%29%29%2F%282%2A%281%29%29+\"\r\n" );
document.write( "\"x+=+%284+%2B-+sqrt%2816-4%29%29%2F2+\"\r\n" );
document.write( "\"x+=+%284+%2B-+sqrt%2812%29%29%2F2+\" \r\n" );
document.write( "\"x+=+%284+%2B-+sqrt%284%2A3%29%29%2F2+\"\r\n" );
document.write( "\"x+=+%284+%2B-+2%2Asqrt%283%29%29%2F2+\"\r\n" );
document.write( "\"x+=+4%2F2+%2B-+2%2Asqrt%283%29%2F2+\"\r\n" );
document.write( "\"x+=+2+%2B-+sqrt%283%29+\"\r\n" );
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document.write( "So the other two zeros are \r\n" );
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document.write( "\"x+=+2+%2B+sqrt%283%29+\" and \"x+=+2+-+sqrt%283%29+\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"x+-+2+-+sqrt%283%29=0+\" and \"x+-+2+%2B+sqrt%283%29+\"\r\n" );
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document.write( "So now \r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29%28x%5E2-4x%2B1%29\"\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "\"%22g%28x%29%22=%28x%2B1%29%28x-2-sqrt%283%29%29%28x-2%2Bsqrt%283%29%29\"\r\n" );
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document.write( "Edwin
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