document.write( "Question 278999: Find the value(s) of \"k\" for which \"k%2B5x%2Bx%5E2\" can be factored.
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Algebra.Com's Answer #202936 by Edwin McCravy(20063)\"\" \"About 
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Find the value(s) of \"k\" for which \"k%2B5x%2Bx%5E2\" can be factored.
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document.write( "Write it in descending order:\r\n" );
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document.write( "\"x%5E2%2B5x%2Bk\"\r\n" );
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document.write( "Suppose it factors as\r\n" );
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document.write( "\"%28x%2Ba%29%28x%2Bb%29\"\r\n" );
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document.write( "Then we can choose a and b as any two integers which\r\n" );
document.write( "add to 5.\r\n" );
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document.write( "We can choose a=1, b=4, or a=2, b=3 \r\n" );
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document.write( "With the first choice,\r\n" );
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document.write( "\"%28x%2Ba%29%28x%2Bb%29\" becomes\r\n" );
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document.write( "\"%28x%2B1%29%28x%2B4%29\"\r\n" );
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document.write( "which when FOILed out becomes\r\n" );
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document.write( "\"x%5E2%2B5x%2B4\", so if k=4 then \"k%2B5x%2Bx%5E2\" can be factored\r\n" );
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document.write( "With the second choice,\r\n" );
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document.write( "\"%28x%2Ba%29%28x%2Bb%29\" becomes\r\n" );
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document.write( "\"%28x%2B2%29%28x%2B3%29\"\r\n" );
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document.write( "which when FOILed out becomes\r\n" );
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document.write( "\"x%5E2%2B5x%2B6\", so if k=6 then \"k%2B5x%2Bx%5E2\" can be factored\r\n" );
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document.write( "So the answer is:  If k = 4 or 6, then \"k%2B5x%2Bx%5E2\" can\r\n" );
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document.write( "be factored.  Otherwise it can't.\r\n" );
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document.write( "Edwin
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