document.write( "Question 1092470: Determine the values of b so that when f(x) is divided by (x-2) the remainder is -2:\r
\n" ); document.write( "\n" ); document.write( "1. f(x)= x^3-bx^2+4x-20
\n" ); document.write( "2. f(x)= -2x^4+40x^2-24x+b
\n" ); document.write( "3. f(x)= x^3-2bx^2+3x-4 \n" ); document.write( "

Algebra.Com's Answer #707080 by ikleyn(52860) $\"\"$ $\"About$

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document.write( "Apply the Remainder theorem.\r\n" );
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document.write( "The remainder theorem says that  \r\n" );
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document.write( "    if a polynomial f(x) is divided by a binomial (x-a), where \"a\" is a constant term (a number), \r\n" );
document.write( "    then the remainder is equal to the value of f(x) at x= a, i.e. f(a).\r\n" );
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document.write( "In your case  a = 2.  By y substituting x= 2 into f(x) you get\r\n" );
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document.write( "    f(2) = 2^3 -b*2^2 + 4*2 - 20 = 8 - 4b + 8 - 20 = -4b - 4.\r\n" );
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document.write( "Therefore, your equation to find \"b\" is\r\n" );
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document.write( "    -4b - 4 = -2    (since -2 is the remainder !)\r\n" );
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document.write( "which implies  4b = 2 - 4 = -2,   b =  = -0.5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. b = -0.5.\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "            Do the other cases in the same way.\r
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\n" ); document.write( "\n" ); document.write( "----------------
\n" ); document.write( "On the Remainder theorem see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Divisibility of polynomial f(x) by binomial x-a\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on the Remainder thoerem\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem\".\r
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