document.write( "Question 630658: Factor the polynomial p(x) = 2x^3-9x^2+7x+6 given the fact that x=2 is a root of the polynomial. \n" ); document.write( "

Algebra.Com's Answer #397138 by jsmallt9(3758) $\"\"$ $\"About$

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If x=2 is a root, then (x-2) is a factor. To find the other factor(s) we divide p(x) by (x-2). This is most easily done with synthetic division. (If you don't know synthetic division then use long division.)

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document.write( "2 |   2   -9    7   6\r\n" );
document.write( "===        4  -10   6\r\n" );
document.write( "     ================\r\n" );
document.write( "      2   -5   -3   0\r\n" );
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\n" ); document.write( "The remainder (in the lower right corner) in zero which means that (x-2) divided evenly. (We should have expected this since factors of something will divide evenly into it.) The rest of the bottom row tells us the other factor. \"2 -5 -3\" translates into $\"2x%5E2-5x-3\"$ . So
\n" ); document.write( " $\"p%28x%29+=+%28x-2%29%282x%5E2-5x-3%29\"$
\n" ); document.write( "We can now use factoring techniques (trinomial factoring) to factor the second factor further:
\n" ); document.write( " $\"p%28x%29+=+%28x-2%29%282x%2B1%29%28x-3%29\"$
\n" ); document.write( "p(x) is now fully factored. \n" ); document.write( "

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