When the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. When it is divided by x - 2, the remainder is -4. What are the values of m and n

Guest Apr 4, 2015

#1**+10 **

When the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1.

When it is divided by x - 2, the remainder is -4. What are the values of m and n

$$\\f(x)=mx^3 - 3x^2 + nx + 2\\

f(-3)=m*-27-3*9+-3n+2=-1\\

-27m-27-3n+2=1\\

-27m-3n-25=1\\

-27m-3n=26\qquad (1)\\\\\\

f(2)=m*8 - 12 + 2n + 2=-4\\

8m - 10 + 2n + 2=-4\\

8m + 2n =4\qquad(2)\\$$

Now check what i have done because it is late and I could easily have made a mistake

Then solve the equations simultaneously. :)

Melody
Apr 4, 2015

#1**+10 **

Best Answer

When the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1.

When it is divided by x - 2, the remainder is -4. What are the values of m and n

$$\\f(x)=mx^3 - 3x^2 + nx + 2\\

f(-3)=m*-27-3*9+-3n+2=-1\\

-27m-27-3n+2=1\\

-27m-3n-25=1\\

-27m-3n=26\qquad (1)\\\\\\

f(2)=m*8 - 12 + 2n + 2=-4\\

8m - 10 + 2n + 2=-4\\

8m + 2n =4\qquad(2)\\$$

Now check what i have done because it is late and I could easily have made a mistake

Then solve the equations simultaneously. :)

Melody
Apr 4, 2015