document.write( "Question 1127209: The remainder of x^3+ax+b when divided by (x^2-1) is x+2. Find a and b. \n" ); document.write( "
Algebra.Com's Answer #743605 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by the tutor @MathLover1 not only is INCORRECT - it is IRRELEVANT, because it operates \r
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\n" ); document.write( "\n" ); document.write( "            with WRONG CONCEPTIONS.   Unfortunately.   Below find the correct solution.\r
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document.write( "From the condition, it should be clear to you that the quotient of division the 3-rd degree polynomial  x^3 + ax + b  \r\n" );
document.write( "by  the quadratic polynomial  (x^2-1)  is a linear polynomial of the form (x+c) with the leading coefficient 1 \r\n" );
document.write( "and the constant term c, now unknown to us.  So\r\n" );
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document.write( "    x^3 + ax + b = (x^2-1)*(x+c) + (x+2).\r\n" );
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document.write( "Now make FOIL, combine like terms and then compare coefficients:\r\n" );
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document.write( "    x^3 + ax + b = x^3 -x + cx^2 - c + x + 2 = x^3 + cx^2 + 2-c.\r\n" );
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document.write( "Comparing coefficients, you see that  c= 0  (look in x^2 !);  a= 0  and  b= 2.\r\n" );
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document.write( "Answer.  a= 0  and b= 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I estime the tutor @MathLover1 very high - she rarely makes mistakes.\r
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\n" ); document.write( "\n" ); document.write( "But even first class tutor is not guaranteed of making mistakes - sometimes :)\r
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