Question 919925
your equation is:


f(x) = x^5 + ax^2 - 2ax + 2


you also know that f(-1) = 4


replace x with -1 in your original equation and you get:


f(-1) = (-1)^5 + a(-1)^2 - 2a(-1) + 2 which becomes:


f(-1) = -1 + a + 2a + 2 which becomes:


f(-1) = 3a + 1


since f(-1) = 4, this means that:


3a + 1 = 4


subtract 1 from both sides of that equation to get:


3a = 3 which results in:


a = 1


that's your solution.


to confirm, replace a in the original equation with 1.


the original equation becomes:


x^5 + x^2 - 2x + 2


f(-1) = (-1)^5 + (-1)^2 - 2(-1) + 2 which becomes:


f(-1) = -1 + 1 + 2 + 2 which becomes:


f(-1) = 4


this agrees with what you were given that f(-1) = 4, so the solution of a = 1 is good.