document.write( "Question 1077643: Rewrite x^4+2x^3+6x^2+5x+6 in the form (x^2+x)^2+a(x^2+x)+b. Fully factorise your answer.\r
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Algebra.Com's Answer #692140 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "If  is identical to (x^2+x)^2+a(x^2+x)+b,\r\n" );
document.write( "then any value substituted for x in both will always give the \r\n" );
document.write( "same answer.\r\n" );
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document.write( "Substituting x=0 in the first gives\r\n" );
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document.write( "Substituting x=0 in the second gives\r\n" );
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document.write( "So b=6\r\n" );
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document.write( "Substituting x=1 in the first gives\r\n" );
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document.write( "Substituting x=1 in the second gives\r\n" );
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document.write( "So 4+2a+b = 20, and since b=6\r\n" );
document.write( "   4+2a+6 = 20\r\n" );
document.write( "    2a+10 = 20\r\n" );
document.write( "       2a = 10\r\n" );
document.write( "        a = 5\r\n" );
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document.write( "So\r\n" );
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document.write( " is identical to  \r\n" );
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document.write( "and we substitute a=5 and b=6:\r\n" );
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document.write( "And that's the form desired.\r\n" );
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document.write( "To factor it let u = x²+x\r\n" );
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document.write( "That factors as\r\n" );
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document.write( "Substitute x²+x for u\r\n" );
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document.write( "Edwin

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