document.write( "Question 1052047: find m such that x+2 is the factor of 3x^3+10x^2+mx+ 14 \n" ); document.write( "

Algebra.Com's Answer #667476 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "find m such that x+2 is the factor of 3x^3+10x^2+mx+ 14
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document.write( "The Remainder Theorem states that (x+2) is the factor of p(x) = 3x^3+10x^2+mx+ 14 if and only is the number -2 is the root of the polynomial p(x).\r\n" );
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document.write( "So, (x+2) is the factor of p(x) if and only if p(-2) = 0.\r\n" );
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document.write( "Therefore, to determine \"m\",  substitute -2 instead of x into the polynomial and equate it to zero:\r\n" );
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document.write( "3*(-2)^3 + 1-*(-2)^2 + m*(-2) + 1 = 0.\r\n" );
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document.write( "It gives you an equation to determine m.\r\n" );
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document.write( "Solve it for m. It will be your answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For the Remainder Theorem see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Divisibility of polynomial f(x) by binomial x-a\r
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