document.write( "Question 595715: Given a polynomail and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.
\n" ); document.write( "X^3+2X^2-33X-90 ; X+5 \n" ); document.write( "

Algebra.Com's Answer #377261 by jsmallt9(3758) $\"\"$ $\"About$

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$\"X%5E3%2B2X%5E2-33X-90\"$
\n" ); document.write( "To find the other factors we start by dividing by the known factor, x+5. I prefer synthetic division over long division:
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document.write( "-5 |   1   2   -33   -90\r\n" );
document.write( "---       -5    15    90\r\n" );
document.write( "     --------------------\r\n" );
document.write( "       1  -3   -18     0\r\n" );
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\n" ); document.write( "The remainder, in the lower right corner, is zero. This is to be expected when x+5 was supposed to be a factor. The other factor is found in the front of the remainder: 1 -3 -18. This translates into $\"x%5E2+-3x+-+18\"$ . Now we just factor that:
\n" ); document.write( " $\"x%5E2-3x-18+=+%28x-6%29%28x%2B3%29\"$

\n" ); document.write( "So your expression, fully factored, is:
\n" ); document.write( " $\"X%5E3%2B2X%5E2-33X-90+=+%28x%2B5%29%28x-6%29%28x%2B3%29\"$ \n" ); document.write( "

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