document.write( "Question 1092373: Determine the value of m so that when f(x) is divided by (x-4) the remainder is -8. f(x)=3x^2+mx+4 \n" ); document.write( "
Algebra.Com's Answer #706978 by ikleyn(52835)\"\" \"About 
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document.write( "According to the Remainder theorem, \r\n" );
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document.write( "    if  f(x) gives the remainder -8  when is divided by (x-4),  then the value f(4) is equal to -8:  f(4) = -8.\r\n" );
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document.write( "So, from the condition, you have THIS  equation to find m:\r\n" );
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document.write( "    3*4^2 +m*4 + 4 = -8.\r\n" );
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document.write( "Simplify and solve for m:\r\n" );
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document.write( "    3*16 + 4m + 4 = -8  ====>  4m = -3*16 - 4 - 8  ====>  4m = -60  ====>  m = \"-60%2F4\" = -15.\r\n" );
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document.write( "Answer.  m = -15.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On the Remainder theorem see the lessons\r
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\n" ); document.write( "\n" ); document.write( "The first lesson contains the Remainder theorem (its formulation and the proof):\r
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document.write( "    Theorem   (the remainder theorem)\r\n" );
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document.write( "    1. The remainder of division the polynomial  \"f%28x%29\"  by the binomial  \"x-a\"  is equal to the value  \"f%28a%29\"  of the polynomial. \r\n" );
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document.write( "    2. The binomial  \"x-a\"  divides the polynomial  \"f%28x%29\"  if and only if the value of  \"a\"  is the root of the polynomial  \"f%28x%29\",  i.e.  \"f%28a%29+=+0\".\r\n" );
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document.write( "    3. The binomial  \"x-a\"  factors the polynomial  \"f%28x%29\"  if and only if the value of  \"a\"  is the root of the polynomial  \"f%28x%29\",  i.e.  \"f%28a%29+=+0\".\r\n" );
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