document.write( "Question 1135045: Let p(x)=9x^3-36x^2-9x+36
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Algebra.Com's Answer #752566 by Edwin McCravy(20055) $\"\"$ $\"About$

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Let p(x)=9x^3-36x^2-9x+36
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document.write( "We use the remainder theorem.  That says the remainder in any synthetic\r\n" );
document.write( "division problem is exactly the same number as you would get if you \r\n" );
document.write( "substituted the number on the far left of the synthetic division into the\r\n" );
document.write( "polynomial.  \r\n" );
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document.write( "3 | 9  -36   -9   36\r\n" );
document.write( "  |     27  -27 -108 \r\n" );
document.write( "    9   -9  -36  -72 \r\n" );
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document.write( "so -72 is the same number as you would get if you substituted the number on the\r\n" );
document.write( "far left of the synthetic division, which is 3, into the polynomial.  And that\r\n" );
document.write( "is what we call P(3).  So P(3) = -72\r\n" );
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document.write( "b. Divide p(x) by x-4 and write p(x)=(x-4)q(x)+r\r\n" );
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document.write( "4 | 9  -36   -9   36\r\n" );
document.write( "  |     36    0  -36 \r\n" );
document.write( "    9    0   -9    0 \r\n" );
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document.write( "The numbers on the bottom row, except the last one determines the quotient\r\n" );
document.write( "polynomial q(x) which is one degree lower than the original.  So the numbers on\r\n" );
document.write( "the bottom of the synthetic division except the last one, 9  0 -9, determines\r\n" );
document.write( "the quotient polynomial which is q(x)=9x³+0x²-9 or q(x)=9x²-9. r=0 and\r\n" );
document.write( "so \r\n" );
document.write( "p(x)=(x-4)q(x)+r  becomes\r\n" );
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document.write( "p(x)=(x-4)(9x²-9)+0\r\n" );
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document.write( "Edwin

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