SOLUTION: determine the value of k so that x-1 is a factor of 3x^3+x^2+2kx+4 *a number with a ^ before the number means that it is an exponent

Question 221774: determine the value of k so that x-1 is a factor of 3x^3+x^2+2kx+4

*a number with a ^ before the number means that it is an exponent
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
If (x-1) is a factor of then it will divide into it evenly. So we will use Synthetic Division to solve this:

1 |    3   1   2k       4
---        3   4     2k+4
       ------------------
       3   4   2k+4  2k+8

The remainder, we can see above, is 2k+8. Since we know that (x-1) divides evenly, the remainder must be zero:
2k+8 = 0
Now we solve this for k. Subtract 8 from both sides:
2k = -8
Divide both sides by 2:
k = -4
RELATED QUESTIONS
Find the value of k if (x-1) is a factor of k^2x^2-2kx-3. (answered by ikleyn)

Find the value of k if (x-1) is a factor of k^2x^2-2kx-3. (answered by Boreal)

Let f(x)=2kx +9, where k is a real number. If f(3):f(6)=1:3, determine the... (answered by stanbon)

Determine the value of k so that 3x-1 is a factor of 3x^3 + 8x^2 + kx -... (answered by greenestamps)

Consider the following. x3 − kx2 + 2kx − 18 Find the value of k such that... (answered by josgarithmetic,MathLover1,MathTherapy)

If ( x + 3) is a factor of x^3 - 2kx + k^2 , then k... (answered by jsmallt9)

Find the Value of k for which the first polynomial is a factor of the second polynomial... (answered by stanbon)

Determine the value of k so that 3x-2 is a factor of 6x^3 + 5x^2 + kx +... (answered by ikleyn,stanbon,solver91311,MathTherapy)

Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor (answered by MathLover1)