document.write( "Question 400453: Factor x^3 + 2x^2– 5x-6 ,given that x +3 is a factor. \n" ); document.write( "

Algebra.Com's Answer #283522 by jsmallt9(3758) $\"\"$ $\"About$

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$\"x%5E3+%2B+2x%5E2-+5x-6\"$
\n" ); document.write( "If x+3 is a factor it will divide evenly into this polynomial. And the quotient will be the other factor. So we divide to find the other factor.

\n" ); document.write( "Synthetic division is easier than long divison for divisors like x+3. You just have to remember that synthetic division is designed for dividing by x-a. So we have to look at x+3 as if it was x-(-3):
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document.write( "-3 |  1   2   -5   -6\r\n" );
document.write( "----     -3    3    6\r\n" );
document.write( "     ----------------\r\n" );
document.write( "      1  -1   -2    0\r\n" );
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\n" ); document.write( "As the zero remainder (in the lower right corner) tells us, x+3 did divide evenly. And the rest of that bottom row tells us what the other factor is. \"1 -1 -2\" tells us the other factor is: $\"x%5E2-x-2\"$ . So
\n" ); document.write( " $\"x%5E3+%2B+2x%5E2-+5x-6+=+%28x%2B3%29%28x%5E2-x-2%29\"$
\n" ); document.write( "The second factor is a trinomial that is simple to factor:
\n" ); document.write( " $\"x%5E3+%2B+2x%5E2-+5x-6+=+%28x%2B3%29%28x%5E2-x-2%29+=+%28x%2B3%29%28x%2B1%29%28x-2%29\"$ \n" ); document.write( "

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