document.write( "Question 1117502: Find the values for a and b for which x³ + ax² -10x + b is
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Algebra.Com's Answer #732605 by Edwin McCravy(20067) $\"\"$ $\"About$

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x³ + ax² - 10x + b is divisible by x² + x - 12
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document.write( "The other solution is correct. Here is an alternate\r\n" );
document.write( "approach:\r\n" );
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document.write( "Since x² + x - 12 can be factored as (x+4)(x-3)\r\n" );
document.write( "which has roots (zeros) x=-4 and x=3. Both must be \r\n" );
document.write( "roots (zeros) of x³ + ax² - 10x + b\r\n" );
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document.write( "So we substitute x=-4 in\r\n" );
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document.write( "   x³ +    ax² -    10x + b\r\n" );
document.write( "(-4)³ + a(-4)² - 10(-4) + b\r\n" );
document.write( " -64  +    16a +     40 + b\r\n" );
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document.write( "and set that equal to 0\r\n" );
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document.write( " -64  +  16a + 40 + b = 0\r\n" );
document.write( "        -24 + 16a + b = 0\r\n" );
document.write( "              16a + b = 24\r\n" );
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document.write( "We also substitute x=3 in\r\n" );
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document.write( "   x³ +   ax² -   10x + b\r\n" );
document.write( " (3)³ + a(3)² - 10(3) + b\r\n" );
document.write( "   27  +   9a -    30 + b\r\n" );
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document.write( "and set that equal to 0\r\n" );
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document.write( "27  +  9a - 30 + b = 0\r\n" );
document.write( "       -3 + 9a + b = 0\r\n" );
document.write( "            9a + b = 3\r\n" );
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document.write( "Then we solve the system of equations;\r\n" );
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document.write( "16a + b = 24\r\n" );
document.write( " 9a + b =  3\r\n" );
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document.write( "Solve that by substitution or elimination\r\n" );
document.write( "and get\r\n" );
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document.write( "a=3 and b = -24    \r\n" );
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document.write( "Edwin

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