Question

Consider the function f(x) = x^3+4x^2+kx-4 the remainder from f(x)/(x+2) is twice the remainder from f(x) /(x-2) determine the the value of k

Answer 1

remainder of f(x)/(x+2), is f(-2) and
remainder of f(x)/(x-2), is f(2).

f(x) = x^3+4x^2+kx-4, thus
f(-2)= (-2)^3 + 4(-2)^2 + k(-2) - 4
f(2)= (2)^3 + 4(2)^2 + k(2) - 4

so, if f(-2)=2f(2) then
(-2)^3 + 4(-2)^2 + k(-2) - 4 = 2( (2)^3 + 4(2)^2 + k(2) - 4 )
simplify,, and solve for k ! goodluck...