Find the values of m and n

Question

When the expression 8x^3+mx^2+nx-9 is divided by x+2 and 2x-3, the remainder are -93 and 6 respectively

Answer 1

We can use synthetic division.

 

-2 | 8          m            n                               -9

 

                 -16        (-2m + 32)           (4m - 2n - 64)

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      8     (m - 16)     (-2m + n + 32)          -93

 

 

 

 

Now we set the process for the other.

 

3/2 | 8               m                   n                        -9

 

                        12          (3/2)m + 18             (9/4)m + (3/2)n + 27

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        8        (m + 12)     (3/2)m + n + 18                 6

 

 

 

The sum in the last column (bolded) of each process make the equations to use to solve for m and n.  These bolded equations are your system of equations.  Use them to solve for m and n.