Question

find m and n if (x+2) and (x+1) are factors of x³+3x²-2mx +n

Answer 1

Value of m= -1 and n= 0

Answer 2

If the given (x+2)and (x+1)
are the factors of the given expression, then x= -2 and x= -1 are the zeros of the given polynomial.
So putting x= -2,
(-2)³+3(-2²) -2m(-2)+n=0
-8+12+4m+n=0
4m+n= - 4......(1)
So putting x= -1,
(-1)³+3(-1²) -2m(-1)+n=0
-1 +3+2m+n=0
2m+n= -2.....(2)
So,ving (1) and (2) We get,
m= -1   and
n= 0
Hope this helps.