document.write( "Question 264952: How to find a “third” first-degree factor of x^3 + 6x^2 – 7x – 60 \n" ); document.write( "

Algebra.Com's Answer #194932 by Edwin McCravy(20056) $\"\"$ $\"About$

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How to find a “third” first-degree factor of $\"x%5E3%2B6x%5E2-7x-60\"$
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document.write( "Since the coefficient of the highest power of x is 1, then if there\r\n" );
document.write( "ia a first degree factor, it will be of the form \r\n" );
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document.write( "x ± r\r\n" );
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document.write( "where r is a factor of the absolute value of the constant term, which\r\n" );
document.write( "in this case is -60.\r\n" );
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document.write( "So we list the factors of |-60|, or 60.  They are\r\n" );
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document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r\n" );
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document.write( "try 1, using synthetic division:\r\n" );
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document.write( "1 | 1  6  -7  -60\r\n" );
document.write( "  |    1   7    0\r\n" );
document.write( "    1  7   0  -60\r\n" );
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document.write( "Nope, that leaves -60 remainder.\r\n" );
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document.write( "try 2, using synthetic division:\r\n" );
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document.write( "2 | 1  6  -7  -60\r\n" );
document.write( "  |    2  16   18\r\n" );
document.write( "    1  8   9  -42\r\n" );
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document.write( "Nope, that leaves -42 remainder.\r\n" );
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document.write( "try 3, using synthetic division:\r\n" );
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document.write( "3 | 1  6  -7  -60\r\n" );
document.write( "  |    3  27   60\r\n" );
document.write( "    1  9  20    0\r\n" );
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document.write( "Yep! That leaves a 0 remainder.\r\n" );
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document.write( "Therefore we have factored  \r\n" );
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document.write( "We got the coefficients in the second parentheses\r\n" );
document.write( "from the numbers 1 9 20 at the bottom of the \r\n" );
document.write( "synthetic division above.\r\n" );
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document.write( "Now we can factor the second parentheses \r\n" );
document.write( "as \r\n" );
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document.write( "And the final factored form is\r\n" );
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document.write( "Edwin

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