document.write( "Question 73065: Can someone please assist me with the below problems. Thank you.\r
\n" ); document.write( "\n" ); document.write( "Christine\r
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\n" ); document.write( "\n" ); document.write( "1) Factor the polynomial into two polynomials of lesser degrees given one of its factors:
\n" ); document.write( "Polynomial: 2x^3 +x^2 - 2x -1; Factor: x + 1\r
\n" ); document.write( "\n" ); document.write( "This is how I attempted to solve:\r
\n" ); document.write( "\n" ); document.write( "1 | 2 1 -2 -1
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\n" ); document.write( "\n" ); document.write( " 2 3 1 0\r
\n" ); document.write( "\n" ); document.write( "Solution: (2x^2 + 3x - 1)(x + 1)\r
\n" ); document.write( "\n" ); document.write( "Please help!!!!!!!\r
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Algebra.Com's Answer #52327 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
You're on the right track by using synthetic division. But the value on in the box should be -1, since x+1=0 x=-1 is your zero\r
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document.write( "          -1 | 2  1  -2  -1\r\n" );
document.write( "               _____________\r\n" );
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document.write( "              2  <---------bring down the first term\r\n" );
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document.write( "          -1 | 2  1  -2  -1\r\n" );
document.write( "               __-2___________   Place the product of (-1) and 2 under the 1\r\n" );
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document.write( "              2  -1              Add the terms\r\n" );
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document.write( "          -1 | 2  1  -2  -1\r\n" );
document.write( "               __-2___1________   Place the product of (-1) and (-1) under the -2\r\n" );
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document.write( "              2  -1   -1           Add the terms\r\n" );
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document.write( "          -1 | 2  1  -2  -1\r\n" );
document.write( "               __-2___1___1_____   Place the product of (-1) and (-1) under the -2\r\n" );
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document.write( "              2  -1   -1   0        Add the terms\r\n" );
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\n" ); document.write( "Since you get a remainder of 0 it shows that x+1 is a zero (which was already given, but we proved it). The qoutient coefficients 2 -1 -1 are then placed next to variables.
\n" ); document.write( " $\"2x%5E2-x-1\"$ So this is your factor
\n" ); document.write( "If you multiplied $\"2x%5E2-x-1\"$ by $\"x%2B1\"$ you would get
\n" ); document.write( " $\"%282x%5E2-x-1%29%28x%2B1%29=2x%5E3+%2Bx%5E2+-+2x+-1\"$ So this is your factored form and your answer.
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