document.write( "Question 1188350: Given f(x)=x^3+kx+2, and x+1 is a factor of f(x), then what is the value of k? \n" ); document.write( "

Algebra.Com's Answer #819416 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Given f(x)=x^3+kx+2, and x+1 is a factor of f(x), then what is the value of k?
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document.write( "The fact that (x+1) is a factor of the polynomial f(x) = x^3 + kx + 2, means that the value of -1\r\n" );
document.write( "is the root of this polynomial: f(-1) = 0,  due to the Remainder theorem.\r\n" );
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document.write( "So, we substitute x= -1 into the polynomial and equate it to zero\r\n" );
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document.write( "    (-1)^3 + k*(-1) + 2 = 0.\r\n" );
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document.write( "It is an equation to determine the value of k.  So, simplify and find k\r\n" );
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document.write( "    -1 -k + 2 = 0\r\n" );
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document.write( "    -1 + 2 = k\r\n" );
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document.write( "     k = 1.\r\n" );
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document.write( "ANSWER.  k = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many other similar (and different) solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Finding unknown coefficients of a polynomial having given info about its polynomial divisors\r
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\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) and the Remainder theorem \r
\n" ); document.write( "\n" ); document.write( "    - Typical problems on the Remainder theorem\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on the Remainder theorem \r
\n" ); document.write( "\n" ); document.write( "    - Finding unknown coefficients of a polynomial having given info about its polynomial divisors\r
\n" ); document.write( "\n" ); document.write( "    - Finding unknown coefficients of a polynomial based on some given info about its roots \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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