SOLUTION: 1.Find the value of k for ehich x^3-2x^2+4x+k has a remainder of -7 when divided by x-1. 2. Find k so that tge remainders is 0 when -x^3+4x^2+kx-2 is divided by x-1. 3. Write a p

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Question 985478: 1.Find the value of k for ehich x^3-2x^2+4x+k has a remainder of -7 when divided by x-1.
2. Find k so that tge remainders is 0 when -x^3+4x^2+kx-2 is divided by x-1.
3. Write a polynomial equation with roots -4,-1, and 6.
4. Write a polynomial equation with roots -2,3, and 5
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
#3:

%28x-%28-4%29%29%28x-%28-1%29%29%28x-6%29
%28x%2B4%29%28x%2B1%29%28x-6%29------multiply if you want.


#1: 

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

k%2B3=7 as specified.
k=7-3
highlight%28k=4%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1.Find the value of k for ehich x^3-2x^2+4x+k has a remainder of -7 when divided by x-1.
That's just like 2 below:

2. Find k so that tge remainders is 0 when -x^3+4x^2+kx-2 is divided by x-1.
Change sign of -1 in x-1 to +1.  Do synthetic division

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

Set remainder k+1 equal to 0 and solve:

k+1 = 0
  k = -1

3. Write a polynomial equation with roots -4,-1, and 6.
     
  x = -4     x = -1      x = 6
x+4 = 0    x+1 = 0     x-6 = 0

     (x+4)(x+1)(x-6) = 0

      (x²+5x+4)(x-6) = 0 

x³-6x²+5x²-30x+4x-24 = 0

        x³-x²-26x-24 = 0

4. Write a polynomial equation with roots -2,3, and 5
That's just like 3 above.

Edwin