The polynomial 6x^3+mx^2+nx-5 has a factor of x+1. When divided by x-1, the remainder is -4. What are m and n?
6 years ago
Perform a synthetic division of polynomial by -1 and since x+1 is a factor, remainder should be zero. That would give you m - n =11
Perform a synthetic division of polynomial by +1 and remainder should be -4. That would give you m + n =-5
Solve the system of 2 equations and 2 unknowns (m,n) which would give you m = 3 and n = -8
We have two unknowns, m and n, so we need to find two equations to solve the problem.
Equation 1 is (6x3+mx2+nx-5)/(x+1) has a remainder of 0
Equation 2 is (6x3+mx2+nx-5)/(x-1) has a remainder of -4
Performing division on Equation 1 gives us that the remainder is -11 - n + m, which is equal to 0.
So now Equation 1 is m-n = 11
Performing division on Equation 2 give us the remainder of n + m + 1 which is equal to -4.
So then Equation 2 become n + m = -5
Combining Equations 1 and 2 togethers gives the final answer of m = 3 and n = -8.