document.write( "Question 1138498: Consider the following polynomial function.\r
\n" ); document.write( "\n" ); document.write( "f(x)=2x3+3x2−12x+7
\n" ); document.write( "Step 1 of 4 : Factor the polynomial completely. \n" ); document.write( "

Algebra.Com's Answer #756328 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "(1) Substitute x=1 to see if x=1 is a root:

\n" ); document.write( " $\"2%2B3-12%2B7+=+0\"$

\n" ); document.write( "Yes, x=1 is a root. Use synthetic division to divide out the factor x-1.

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document.write( "\r\n" );
document.write( " 1  |  2  3  -12  7\r\n" );
document.write( "    |     2    5 -7\r\n" );
document.write( "    +--------------\r\n" );
document.write( "       2  5   -7  0

\n" ); document.write( "The remainder is 0, so x=1 is a root; (x-1) is a factor.

\n" ); document.write( " $\"2x%5E3%2B3x%5E2-12x%2B7+=+%28x-1%29%282x%5E2%2B5x-7%29\"$

\n" ); document.write( "(2) Factor the remaining quadratic by whatever method you know.

\n" ); document.write( " $\"2x%5E3%2B3x%5E2-12x%2B7+=+%28x-1%29%282x%2B7%29%28x-1%29\"$
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