document.write( "Question 716670: using synthetic division solve
\n" ); document.write( "(5x^2 - 12x - 8)/(x + 3) \n" ); document.write( "

Algebra.Com's Answer #439954 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%285x%5E2+-+12x+-+8%29%2F%28x+%2B+3%29\"$
\n" ); document.write( "is just an expression and expressions cannot be \"solved\". But they can be simplified. In this case we can divide the numerator by the denominator.

\n" ); document.write( "Synthetic division is designed for division by an expression of the form:
\n" ); document.write( "x - n
\n" ); document.write( "where \"n\" is some number. If we are to use synthetic division to divide by x+3 we must imagine (or actually rewrite) it as a subtraction: x - (-3):
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document.write( "-3  |   5   -12   -8\r\n" );
document.write( "-----       -15   81\r\n" );
document.write( "       -------------\r\n" );
document.write( "        5   -27   73\r\n" );
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The remainder is in the lower right corner. It is 73. The rest of the bottom row is the quotient. The \"5 -27\" translates into 5x-27. So after dividing:
\n" ); document.write( " $\"%285x%5E2+-+12x+-+8%29%2F%28x+%2B+3%29\"$
\n" ); document.write( "we get:
\n" ); document.write( " $\"5x-27%2B73%2F%28x%2B3%29\"$
\n" ); document.write( "(Note what happens with the remainder. We handle in just the same way as in the \"good old days\" before variables: We make a fraction with the remainder on top and the divisor on the bottom!) \n" ); document.write( "

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