document.write( "Question 221774: determine the value of k so that x-1 is a factor of 3x^3+x^2+2kx+4\r
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\n" ); document.write( "\n" ); document.write( "*a number with a ^ before the number means that it is an exponent \n" ); document.write( "

Algebra.Com's Answer #166240 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
If (x-1) is a factor of $\"3x%5E3%2Bx%5E2%2B2kx%2B4\"$ then it will divide into it evenly. So we will use Synthetic Division to solve this:
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document.write( "1 |    3   1   2k       4\r\n" );
document.write( "---        3   4     2k+4\r\n" );
document.write( "       ------------------\r\n" );
document.write( "       3   4   2k+4  2k+8\r\n" );
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\n" ); document.write( "The remainder, we can see above, is 2k+8. Since we know that (x-1) divides evenly, the remainder must be zero:
\n" ); document.write( "2k+8 = 0
\n" ); document.write( "Now we solve this for k. Subtract 8 from both sides:
\n" ); document.write( "2k = -8
\n" ); document.write( "Divide both sides by 2:
\n" ); document.write( "k = -4 \n" ); document.write( "

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