document.write( "Question 235868: determine whether the iven number is a zero of the polynomials.
\n" ); document.write( "2, $\"P%28x%29=x%5E3%2B2x%5E2-29x%2B42\"$ \r
\n" ); document.write( "\n" ); document.write( "p(x)=x to the third power+two x to the second power+ twentynine x+fourty two \n" ); document.write( "

Algebra.Com's Answer #173633 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Substitute 2 for x in \r\n" );
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document.write( "and see if we get 0.  If so, 2 is a zero of P(x).\r\n" );
document.write( "But if not, 2 is not a zero of P(x).\r\n" );
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document.write( "Yes, 2 is a zero of P(x), for we got 0 when we \r\n" );
document.write( "substituted 2 for x.\r\n" );
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document.write( "Maybe your teacher wanted you to use the synthetic\r\n" );
document.write( "division method for substituting instead of\r\n" );
document.write( "directly substituting. If so then use this method\r\n" );
document.write( "for substituting 2 instead of directly substituting.\r\n" );
document.write( "Write the 2 on the left and the coefficients of x\r\n" );
document.write( "in order on the right, and draw this array:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |\r\n" );
document.write( "      --------------\r\n" );
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document.write( "Bring down the 1\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1\r\n" );
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document.write( "Multiply the 1 by the 2 on the left,\r\n" );
document.write( "getting 2, and write it above and to the right\r\n" );
document.write( "of the 1, under the upper 2, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1\r\n" );
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document.write( "Now add the 2+2, getting 4 and write it below the\r\n" );
document.write( "two 2's beside the 1, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1  4\r\n" );
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document.write( "Multiply the 4 by the 2 on the left,\r\n" );
document.write( "getting 8, and write it above and to the right\r\n" );
document.write( "of the 4, under the -29, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2    8\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1  4\r\n" );
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document.write( "Now add the -29+8, getting -21 and write it below the\r\n" );
document.write( "-29 and the 8 beside the 4, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2    8\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1  4  -21\r\n" );
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document.write( "Multiply the -21 by the 2 on the left,\r\n" );
document.write( "getting -42, and write it above and to the right\r\n" );
document.write( "of the -21, under the 42, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2    8 -42\r\n" );
document.write( "      --------------\r\n" );
document.write( "       1  4  -21\r\n" );
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document.write( "Now add the 42-42, getting 0 and write it below the\r\n" );
document.write( "42 and the -42 beside the -21, like this:\r\n" );
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document.write( "   2 | 1  2  -29  42\r\n" );
document.write( "     |    2    8 -42 \r\n" );
document.write( "      --------------\r\n" );
document.write( "       1  4  -21   0\r\n" );
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document.write( "That bottom right number is always the same as what\r\n" );
document.write( "you get when you substitute 2 for x in the polynomial.\r\n" );
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document.write( "The reason your teacher wants you to learn this method\r\n" );
document.write( "for substituting, instead of the easier method of \r\n" );
document.write( "directly substituting is because synthetic division has\r\n" );
document.write( "other uses, and sometimes it's actually easier than\r\n" );
document.write( "directly substituting.\r\n" );
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document.write( "Edwin

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