Asap when 2x^3 -mx^2 + nx-2 is divided by x+1, the remainder is -12 and x-2 is a factor. determine the values of m and n.

m = 5 and n = 3

let f(x) = 2x³ - mx² + nx - 2 , then

f( - 1 ) = - 2 - m - n - 2 = - 12

f(2 ) = 16 - 4m + 2n - 2 = 0

Tidying up the 2 equations

- m - n = - 8 → (1)

- 4m + 2n = - 14 → ( 2)

multiply equation ( 1) by 2

- 2m - 2n = - 16 → ( 3 )

add ( 2 ) and ( 3 ) term by term

-6m = - 30 ⇒ m = 5 ( substitute m = 5 into (2 )

- 20 + 2n = - 14

2n = 6 ⇒ n = 3

m∠a is 90°

m∠b is 40°