If mx^3+(n-5)x^2+3x-1 is divided by (x-2) , the remainder is -11 and it has a factor of (x-1), find the values of m and n.
+130536 If mx^3+(n-5)x^2+3x-1 is divided by (x-2) , the remainder is -11 and it has a factor of (x-1), find the values of m and n
If x - 1 is a factor, then 1 is a root.....and we have.....
m + n - 5 + 3 - 1 = 0 simplify
m + n - 3 = 0 → n = 3 - m
And we know that f(2) = 11 .....so....
m(2)^3 + ( 3 - m - 5)(2)^2 + 3(2) - 1 = 11 simplify
8m + (-2 - m)(4) + 6 - 1 = 11
8m -8 - 4m + 6 - 1 = 11
4m - 3 = 11 → m = 7/2 and n = 3 - 7/2 = -1/2
Here's a graph of the function : https://www.desmos.com/calculator/vsp5mk19bj
