document.write( "Question 1048380: if X^4+aX^3-3X^2+2aX+a^2 is aperfect square and has a factor (X+2). find (a), when (a) has this vàlue to obtain the square root of the expression in its factorized form \n" ); document.write( "
Algebra.Com's Answer #663950 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
This must be an identity\r\n" );
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document.write( "\"x%5E4%2Bax%5E3-3x%5E2%2B2ax%2Ba%5E2\"\"%22%22=%22%22\"\"%28%28x%2B2%29%28x%2Bk%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "If x=0\r\n" );
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document.write( "\"%280%29%5E4%2Ba%280%29%5E3-3%280%29%5E2%2B2a%280%29%2Ba%5E2\"\"%22%22=%22%22\"\"%28%28%280%29%5E%22%22%2B2%29%28%280%29%5E%22%22%2Bk%29%5E%22%22%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2\"\"%22%22=%22%22\"\"%282k%29%5E2\"\r\n" );
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document.write( "\"a\"\"%22%22=%22%22\"\"%22%22+%2B-+2k\"\r\n" );
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document.write( "If x=1\r\n" );
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document.write( "\"%281%29%5E4%2Ba%281%29%5E3-3%281%29%5E2%2B2a%281%29%2Ba%5E2\"\"%22%22=%22%22\"\"%28%28%281%29%5E%22%22%2B2%29%28%281%29%5E%22%22%2Bk%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "\"1%2Ba-3%2B2a%2Ba%5E2\"\"%22%22=%22%22\"\"%28%281%2B2%29%281%2Bk%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "\"1%2Ba-3%2B2a%2Ba%5E2\"\"%22%22=%22%22\"\"%283%281%2Bk%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "\"1%2Ba-3%2B2a%2Ba%5E2\"\"%22%22=%22%22\"\"9%281%2Bk%29%5E2\"\r\n" );
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document.write( "Substituting \"a\"\"%22%22=%22%22\"\"2k\"\r\n" );
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document.write( "\"1%2B%282k%29-3%2B2%282k%29%2B%282k%29%5E2\"\"%22%22=%22%22\"\"9%281%2Bk%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"4k%5E2%2B6k-2\"\"%22%22=%22%22\"\"9k%5E2%2B18k%2B9\"\r\n" );
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document.write( "\"-5k%5E2-12k-11\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"5k%5E2%2B12k%2B11\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Discriminant = \"12%5E2-4%2A5%2A11=144-220=-76\"\r\n" );
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document.write( "So it has imaginary solutions.  We ignore \"a\"\"%22%22=%22%22\"\"2k\"\r\n" );
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document.write( "Substituting \"a\"\"%22%22=%22%22\"\"-2k\"\r\n" );
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document.write( "\"1%2B%28-2k%29-3%2B2%28-2k%29%2B%28-2k%29%5E2\"\"%22%22=%22%22\"\"9%281%2Bk%29%5E2\"\r\n" );
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document.write( "\"1-2k-3-4k%2B4k%5E2\"\"%22%22=%22%22\"\"9%281%2B2k%2Bk%5E2%29\"\r\n" );
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document.write( "\"4k%5E2-6k-2\"\"%22%22=%22%22\"\"9k%5E2%2B18k%2B9\"\r\n" );
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document.write( "\"-5k%5E2-24k-11\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"5k%5E2%2B24k%2B11\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "Discriminant = \"24%5E2-4%2A5%2A11=576-220=356\"\r\n" );
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document.write( "That has real solutions\r\n" );
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document.write( "\"5k%5E2%2B24k%2B11\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%28-24+%2B-+sqrt%2824%5E2-4%2A5%2A11+%29%29%2F%282%2A5%29+\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%28-24+%2B-+sqrt%28356+%29%29%2F10+\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%28-24+%2B-+sqrt%284%2A89%29%29%2F10+\"\r\n" );
document.write( "\r\n" );
document.write( "\"k\"\"%22%22=%22%22\"\"%28-24+%2B-+2sqrt%2889%29%29%2F10+\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%282%28-12+%2B-+sqrt%2889%29%29%29%2F10+\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%28-12+%2B-+sqrt%2889%29%29%2F5+\" \r\n" );
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document.write( "\"a\"\"%22%22=%22%22\"\"-2k\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"%28-12+%2B-+sqrt%2889%29%29%2F5+\"\r\n" );
document.write( "\r\n" );
document.write( "\"a\"\"%22%22=%22%22\"\"-2%2Aexpr%28%28-12+%2B-+sqrt%2889%29%29%2F5%29+\"\r\n" );
document.write( "\r\n" );
document.write( "\"a\"\"%22%22=%22%22\"\"%2824+%2B-+2sqrt%2889%29%29%2F5+\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"%28%28x%2B2%29%28x%2Bk%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "\"%28%28x%2B2%29%28x%2B%28%28-12+%2B-+sqrt%2889%29%29%2F5%29%29%5E%22%22%29%5E2\"\r\n" );
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document.write( "\"expr%281%2F25%29%28%28x%2B2%29%5E%22%22%285x-sqrt%2889%29-12%29%29%5E2\"\r\n" );
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document.write( "Edwin
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