Question

If x3+mx2-x+6 has (x-2) as a factor and leaves a remainder ‘n’ when divided by (x-3) , find the value of m and n .

Answer 1

Let the polynomial: x^3 +mx^2-x+6 be f(x)
 As the polynomial has (x-2) as a factor therefore 2 is one of the root/zero of the polynomial. On replacing x with 2 we get f(x)=0
f(x)= x^3 +mx^2-x+6
f(2)=8+4m-2+6=0
4m= -12
m= -3
therefore the polynomial is x^3-3x^2-x+6
when the polynomial is divided by (x-3)
x^3-3x^2-x+6=(x-3)quotient+remainder            {euclid's division algorithm}
as remainder = n and replacing x by 3
we get,
27-18-3+6= (3-3)quotient+n
n=12

Answer 2

here is your answer

I hope it will help u