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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
If (x-1) is a factor of 3x%5E3%2Bx%5E2%2B2kx%2B4 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