document.write( "Question 624139: Use synthetic division to find P(–2) for P(x) = x^4 + 9x^3 - 9x + 2 .
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\n" ); document.write( "A. –2
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\n" ); document.write( "B. 0
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\n" ); document.write( "C. –36
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\n" ); document.write( "D. 68 \r
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Algebra.Com's Answer #392568 by jsmallt9(3758) $\"\"$ $\"About$

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The straightforward approach to finding P(-2) is to replace all the x's with -2's and then simplify. But this process can be tedious: raising -2 to various powers and then do all that adding and /or subtracting.

\n" ); document.write( "Synthetic division is a quick, fairly simple way to divide a polynomial by something of the form (x-a). And the Remainder Theorem tells us that for any polynomial, P(x), P(a) will be the remainder of $\"P%28x%29%2F%28x-a%29\"$ . These facts combine to explain why we can use synthetic division to find the value of a polynomial. It is often much easier this way to find P(a) than the straightforward approach described above.

\n" ); document.write( "Probably the easiest way to get this wrong is to fail to notice that there is no $\"x%5E2\"$ term. When we set up the synthetic division we must notice this and know to use a 0 for its coefficient:
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document.write( "-2 |   1   9    0   -9    2\r\n" );
document.write( "===       -2  -14   28  -38\r\n" );
document.write( "      =====================\r\n" );
document.write( "       1   7  -14   19  -36\r\n" );
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\n" ); document.write( "The remainder of this division is always in the lower right corner. So your remainder, and therefore P(-2), is -36. \n" ); document.write( "

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