document.write( "Question 985333: 1.) Explain the difference between using the remainder theorem and synthetic division in finding the remainder when P(x) is divided by x-r. \n" ); document.write( "
Algebra.Com's Answer #606139 by Edwin McCravy(20056)\"\" \"About 
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document.write( "I think you're asking what is the difference between the \r\n" );
document.write( "remainder theorem and the factor theorem?\r\n" );
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document.write( "The Remainder Theorem:\r\n" );
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document.write( "When we divide a polynomial f(x) by x-c the remainder equals f(c)\r\n" );
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document.write( "The Factor Theorem:\r\n" );
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document.write( "When f(c)=0 then x-c is a factor of the polynomial\r\n" );
document.write( "When x-c is a factor of the polynomial then f(c)=0\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "1.  Use the remainder theorem to find what you get when you substitute\r\n" );
document.write( "    -3 for x in f(x) = 3x^3 - 5x^2 + 7x - 4, whch is f(-3).  Then check \r\n" );
document.write( "    your answer by actually substituting -3 in f(x) to find f(-3)\r\n" );
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document.write( "    -3 | 3   -5    7    -4\r\n" );
document.write( "       |     -9   42  -147\r\n" );
document.write( "         3  -14   49  -151\r\n" );
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document.write( "So f(-3) = -151, the number in the lower right corner of the synthetic division. \r\n" );
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document.write( "Checking by actually substituting -3 for x in f(x)\r\n" );
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document.write( "f(x) = 3x^3 - 5x^2 + 7x - 4\r\n" );
document.write( "f(-3) = 3(-3)^3 - 5(-3)^2 + 7(-3) - 4\r\n" );
document.write( "f(-3) = 3(-27) - 5(9) -21 - 4\r\n" );
document.write( "f(-3) = -81 - 45 - 21 - 4\r\n" );
document.write( "f(-3) = -151\r\n" );
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document.write( "2.  Use the factor theorem to show that x-2 is a factor of x^4-7x^2+x+10\r\n" );
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document.write( "2 | 1  0 -7  1  10\r\n" );
document.write( "  |    2  4 -6 -10 \r\n" );
document.write( "    1  2 -3 -5   0\r\n" );
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document.write( "Edwin
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