document.write( "Question 1204305: Determine whether the binomial (3x - 2) is a factor of the polynomial $\"3x%5E3-14x%5E2%2B26x-12\"$ \r
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Algebra.Com's Answer #840463 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(3x-2) is a factor of the polynomial if x=2/3 makes the function value zero.

\n" ); document.write( "Since no method was specified, here are three....

\n" ); document.write( "(1) Graph the function on a graphing calculator and evaluate the function at x=2/3 and see that the function value is 0.

\n" ); document.write( "That's fine...but you don't learn any skills by doing it that way.

\n" ); document.write( "(2) With pencil and paper, evaluate the function for x=2/3:

\n" ); document.write( " $\"3%282%2F3%29%5E3-14%282%2F3%29%5E2%2B26%282%2F3%29-12\"$
\n" ); document.write( " $\"3%288%2F27%29-14%284%2F9%29%2B26%282%2F3%29-12\"$
\n" ); document.write( " $\"24%2F27-56%2F9%2B52%2F3-12\"$
\n" ); document.write( " $\"8%2F9-56%2F9%2B52%2F3-12\"$
\n" ); document.write( " $\"-48%2F9%2B52%2F3-12\"$
\n" ); document.write( " $\"-16%2F3%2B52%2F3-12\"$
\n" ); document.write( " $\"36%2F3-12\"$
\n" ); document.write( " $\"12-12\"$
\n" ); document.write( " $\"0\"$

\n" ); document.write( "Good exercise in arithmetic....

\n" ); document.write( "(3) Use synthetic division to verify that x=2/3 is a zero of the function.

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document.write( "      |   3 -14  26 -12\r\n" );
document.write( "  2/3 |       2  -8  12\r\n" );
document.write( "      +-----------------\r\n" );
document.write( "          3 -12  18   0

\n" ); document.write( "Synthetic division is a useful skill to have...

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