Question

when 10x^3+mx^2-x+10 is divided by 5x-3, the quotient is 2x^2 +nx-2 and the remainder is 4. Find the values of m and n.

Answer 1

`(10x ^(3) +mx^2- x +10 )/(5x -3) = 2x^2 +nx -2 +4`
=
`(10x ^(3) +mx^2- x +10 )/(5x -3) = 2x^2 +nx +2`
=
`10x ^(3) +mx^2- x +10= (2x^2 +nx +2)(5x -3)`
=
`10x ^(3) +mx^2- x +10=10x^3 + 5nx^2 +10x -6x^2 -3nx -6`
=
`mx^2- x +10= + 5nx^2 +10x -6x^2 -3nx -6`
=
`mx^2- x +10=(5n-6)x^2 +(10 -3n)x -6`
=
`(5n-6-m)x^2 +(10 -3n+1)x -16`
=
`(5n-6-m)x^2 +(11-3n)x -16`