document.write( "Question 696488: The expressions x³+ax²-x+b and x³+bx²-5x+3a have a common factor x+2. Find the value of a and b. \n" ); document.write( "

Algebra.Com's Answer #429060 by Edwin McCravy(20067) $\"\"$ $\"About$

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The expressions x³+ax²-x+b and x³+bx²-5x+3a have a common factor x+2. Find the value of a and b.
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document.write( "Since each has a common factor of x+2, -2 is a zero \r\n" );
document.write( "of each polynomial.  Therefore if we substitute x=-2\r\n" );
document.write( "in each we will get 0.\r\n" );
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document.write( "                   x³+ax²-x+b      x³+bx²-5x+3a\r\n" );
document.write( "          (-2)³+a(-2)²-(-2)+b=0    (-2)³+b(-2)²-5(-2)+3a=0\r\n" );
document.write( "                  -8+a(4)+2+b=0            -8+b(4)+10+3a=0\r\n" );
document.write( "                      -6+4a+b=0                  2+4b+3a=0\r\n" );
document.write( "                         4a+b=6                    3a+4b=-2                     \r\n" );
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document.write( "Solve the system of equation:\r\n" );
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document.write( "4a+ b= 6\r\n" );
document.write( "3a+4b=-2\r\n" );
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document.write( "Get a=2, b=-2.\r\n" );
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document.write( "Edwin

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