document.write( "Question 252123: Determine the value of k so that x^2 –3x – 4k divides x^3 –37x –12k \n" ); document.write( "
Algebra.Com's Answer #183919 by drk(1908)\"\" \"About 
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To solve this problem, we want to use polynomial division. On the outside you will write \"x%5E2-3x-4k\" and on the inside you will write \"x%5E3+%2B+0x%5E2+-37x+-12k\". Notice that there is a 0x^2. This is because we jumped over the x^2 term. Now we are ready to divide. \r
\n" ); document.write( "\n" ); document.write( "In the first division run through, we place an x above the x^3 term. By distributive property, we get \"x%5E3+-3x%5E2+-4kx\". Now by subtraction, your new level of terms is \"3x%5E2+-+37x+%2B+4kx\". Bring down the -12k and redivide. This time we place a 3 above the 0x^2 term and distribute as before to get
\n" ); document.write( "\"3x%5E2+-+9x+-+12k\". This subtracts nicely to get -28x + 4kx. The remainder must be zero, so
\n" ); document.write( "-28x - 4kx = 0. K = -7.
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