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

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(52787)   (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.
------
3x-2 is a factor if x = 2/3 is a zero.
------
Solve for "k"::
-----------------------
6(2/3)^3 + 5(2/3)^2 + (2/3)k + 10 = 0
------------------------------------------
6(8/27) + 5(4/9) + (2/3)k + 10 = 0
------
Multiply thru by 27 to get:
48 + 60 + 36k + 270 = 0
36k = -378
-----
k = -10.5
-----------------
Cheers,
Stan H.
-------------
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
RELATED QUESTIONS
Determine the value of k so that 3x-1 is a factor of 3x^3 + 8x^2 + kx -... (answered by greenestamps)
Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor (answered by MathLover1)
Find the value of k such that x-2 is a factor of kx^3 - kx^2 + x+2 (answered by ikleyn)
Find the value of k so that (x-5) is a factor of kx^3 - 17x^2 - 4kx +... (answered by josgarithmetic)
1. Find k so that x+5 is a factor of x^3+5x^2-kx-20. 2. Find k so that x-7 is a factor... (answered by Edwin McCravy)
If (x + 2) is a factor of x^3 − 6x^2 + kx + 10, k... (answered by stanbon)
Find k such that x+2 is a factor of... (answered by robertb)
if x+1 is a factor of x^3+3x^2+kx+4, find the value of... (answered by Boreal,ikleyn)
Determine the value of k in f(x)=2x^3+kx^2-28x-15 such that x-3 is a factor. (answered by josgarithmetic)