document.write( "Question 596013: Use synthetic division to divide the polynomial (2x^3+11x^2-2x-25) divided by the linear factor (2x+3) and state in the from Q(x)+r(x) where r(x) is the remainder. \n" ); document.write( "
Algebra.Com's Answer #377500 by Edwin McCravy(20060)\"\" \"About 
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Use synthetic division to divide the polynomial (2x^3+11x^2-2x-25) divided by the linear factor (2x+3) and state in the from Q(x)+r(x) where r(x) is the remainder.
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document.write( "Synthetic division is only for division by x-r, where the coefficient\r\n" );
document.write( "of x is 1.  So to use synthetic division when the coefficient of x\r\n" );
document.write( "is not 1, you must first write the division as a fraction:\r\n" );
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document.write( "\"%282x%5E3%2B11x%5E2-2x-25%29%2F%282x%2B3%29\"\r\n" );
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document.write( "Then factor out the coefficient x, in this case 2, in the bottom\r\n" );
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document.write( "(Yes I know you were taught that you couldn't factor anything out of\r\n" );
document.write( "2x+3, but they meant that you couldn't factor anything out of it without\r\n" );
document.write( "running into fractions, but you're a big boy or girl now :) and you\r\n" );
document.write( "can handle fractions.  So factor out 2, and get \"2%28x%2B3%2F2%29%29\" and put\r\n" );
document.write( "up with a fraction inside the parentheses: \r\n" );
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document.write( "\"%282x%5E3%2B11x%5E2-2x-25%29%2F%282%28x%2B3%2F2%29%29\"\r\n" );
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document.write( "Now consider that coefficient 2 you factored out on the boottom \r\n" );
document.write( "as amounting to multiplication by the fraction \"1%2F2\": \r\n" );
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document.write( "\"expr%281%2F2%29\"×\"%282x%5E3%2B11x%5E2-2x-25%29%2F%28x%2B3%2F2%29\"\r\n" );
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document.write( "We will do the fraction by synthetic division and \r\n" );
document.write( "then divide through by 2\r\n" );
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document.write( "-\"3%2F2\"⃒ 2  11  -2  -25\r\n" );
document.write( "  ⃒    -3 -12   21  \r\n" );
document.write( "    2   8 -14   -4\r\n" );
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document.write( "This quotient is 2x² + 8x - 14 + \"%28-4%29%2F%28x%2B3%2F2%29\"\r\n" );
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document.write( "Then we multiply by 1/2 and get:\r\n" );
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document.write( "        x² + 4x - 7 + \"%28-2%29%2F%28x%2B3%2F2%29\" \r\n" );
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document.write( "We can simplify the fraction by multiplying top and bottom\r\n" );
document.write( "by 2\r\n" );
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document.write( "        x² + 4x - 7 + \"%28-4%29%2F%282x%2B3%29\"\r\n" );
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document.write( "And then we can just put a minus sign and make the numerator 4\r\n" );
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document.write( "        x² + 4x - 7 - \"4%2F%282x%2B3%29\"\r\n" );
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document.write( "Edwin
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