document.write( "Question 1205720: what is the remainder when P(x)=x^(2)+5 is divided by (x+1)
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Algebra.Com's Answer #842711 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " I will show you two ways of solving this problem.\r
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document.write( "       First way: using the remainder theorem\r\n" );
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document.write( "According to the Remainder theorem, the remainder of division any polynomial P(x)\r\n" );
document.write( "by a binomial (x-a), where \"a\" is a real (or integer) number, is the value \r\n" );
document.write( "of the polynomial P(x) at x= a, i.e. P(a).\r\n" );
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document.write( "In this problem, a= -1, so, according to the Remainder theorem, the remainder \r\n" );
document.write( "of division P(x) = x^2+5 by (x+1) is P(-1) = (-1)^2 + 5 = 6.\r\n" );
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document.write( "ANSWER.  The remainder of division P(x) = x^2+5  by  (x+1)  is  6.\r\n" );
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document.write( "       Second way: using explicit division via grouping\r\n" );
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document.write( "Using grouping, we can write\r\n" );
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document.write( "    P(x) =  =  +  = x(x+1)  + (-x-1) + 1 + 5 = x(x+1) - (x+1) + 6 = \r\n" );
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document.write( "         = (x+1)*(x-1) + 6.\r\n" );
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document.write( "It shows that when P(x) is divided by (x+1), the quotient is (x-1) and the remainder is 6.\r\n" );
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document.write( "Thus the ANSWER is the same as in the first solution above.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in two ways for your better understanding.\r
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\n" ); document.write( "\n" ); document.write( "Surely, there is third way, which is direct long division of polynomials.\r
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\n" ); document.write( "\n" ); document.write( "This method is straightforward and purely mechanical procedure - therefore,
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