SOLUTION: 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 of x^3-4x^2-kx-14. 3. Find k so that x+9 is a factor if x^3+kx^2+3x-54.

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: 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 of x^3-4x^2-kx-14. 3. Find k so that x+9 is a factor if x^3+kx^2+3x-54.      Log On

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Question 985475: 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 of x^3-4x^2-kx-14.
3. Find k so that x+9 is a factor if x^3+kx^2+3x-54.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
3. Find k so that x+9 is a factor if x^3+kx^2+3x-54.

Change sign of +9 in k+9 to -9.  Do synthetic division:

-9 | 1    k       3      -54
   |     -9  -9k+81  81k-756
     1  k-9  -9k+84  81k-810

Set remainder 81k-810 = 0
                  81k = 810
                    k = 10

The others are done the same way.

Edwin