SOLUTION: Determine the value of k so that 3x-2 is a factor of 6x^3 + 5x^2 + kx + 10.

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Question 995825: Determine the value of k so that 3x-2 is a factor of 6x^3 + 5x^2 + kx + 10.
Found 4 solutions by ikleyn, stanbon, solver91311, MathTherapy:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website!
.
If 3x-2 is a factor of , then this polynomial has the root .

So, substitute in place of x, and you will get the equation to determine k.

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Determine the value of k so that 3x-2 is a factor of 6x^3 + 5x^2 + kx + 10.
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3x-2 is a factor if x = 2/3 is a zero.
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Solve for "k"::
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6(2/3)^3 + 5(2/3)^2 + (2/3)k + 10 = 0
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6(8/27) + 5(4/9) + (2/3)k + 10 = 0
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Multiply thru by 27 to get:
48 + 60 + 36k + 270 = 0
36k = -378
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k = -10.5
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Cheers,
Stan H.
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Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

If is a factor of the polynomial, so is . Use Synthetic Division

2/3 6 5 k 10 4 6 -10 ----------------------- 6 9 ? 0

So . Solve for

John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Determine the value of k so that 3x-2 is a factor of 6x^3 + 5x^2 + kx + 10.

After applying long division, itw's determined that:
kx + 6x = - 15x
x(k + 6) = x(- 15) -------- Factoring out GCF, x
k + 6 = - 15
k = - 15 - 6, or