document.write( "Question 1088858: If x+2 is a factor of x^3 - ax- 6,then find the remainder when 2x^3+ax^2-6x+9 is divided by x+1.
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Algebra.Com's Answer #703256 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "If x+2 is a factor of x^3 - ax- 6,then find the remainder when 2x^3+ax^2-6x+9 is divided by x+1.
\n" ); document.write( "Please help me with this question.
\n" ); document.write( "Thank You.
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\n" ); document.write( "\n" ); document.write( "Let me do it in a way in how it SHOULD BE DONE.\r
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document.write( "1.  If (x+2) is a factor of , then, according to the Remainder theorem, the number -2 is the root of the polynomial p(x) = .\r\n" );
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document.write( "    In other words, p(-2) = 0,  which means\r\n" );
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document.write( "     = 0,   or, simplifying,\r\n" );
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document.write( "    -8 + 2a - 6 = 0,   or   2a = 8 + 6 = 14  ====>  a =  = 7.\r\n" );
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document.write( "3.  Hence, the second polynomial is \r\n" );
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document.write( "    q(x) = .\r\n" );
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document.write( "    Then,  again, due to the Remainder theorem, the remainder of division q(x) by (x+1) is equal to the value q(-1), i.e.\r\n" );
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document.write( "     q(-1) =  = 2*(-1) + 7*1 + 6 + 9 = 20.\r\n" );
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document.write( "Answer. The remainder of division the second polynomial by (x+1) is 20.\r\n" );
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\n" ); document.write( "The remainder theorem:\r
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document.write( "    1. The remainder of division the polynomial    by the binomial    is equal to the value    of the polynomial. \r\n" );
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document.write( "    2. The binomial    divides the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .\r\n" );
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document.write( "    3. The binomial    factors the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is 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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\n" ); document.write( "Ignore writing by @josgarithmetic. His way IS NOT the method for solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "It is not his level of knowledge and is not his area of expertise.\r
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