Question 252123: Determine the value of k so that x^2 –3x – 4k divides x^3 –37x –12k Found 2 solutions by drk, edjones:Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! To solve this problem, we want to use polynomial division. On the outside you will write and on the inside you will write . Notice that there is a 0x^2. This is because we jumped over the x^2 term. Now we are ready to divide.
In the first division run through, we place an x above the x^3 term. By distributive property, we get . Now by subtraction, your new level of terms is . Bring down the -12k and redivide. This time we place a 3 above the 0x^2 term and distribute as before to get . This subtracts nicely to get -28x + 4kx. The remainder must be zero, so
-28x - 4kx = 0. K = -7.
You can put this solution on YOUR website! ....................... x+3
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x^2-3x-4k/x^3..........-37x-12k
.....................x^3-3x^2-4kx
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............................3x^2-9x-12k
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-37x-(-4kx)=-9x
-37+4k=-9 divide each side by x.
4k=37-9
4k=28
k=7
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Ed
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