If the function f(fx) = x3 + 2x2 + qx - 6 is divisible by x + 1, find q
Answer Details
To find the value of q, we can use the fact that the given function f(fx) is divisible by x+1.
If a polynomial f(x) is divisible by x-a, then f(a) = 0.
Using this fact, we can substitute x = -1 in the given function f(fx) = x^3 + 2x^2 + qx - 6, since x+1 is a factor of f(fx):
f(f-1) = (-1)^3 + 2(-1)^2 + q(-1) - 6
f(f-1) = -1 + 2 - q - 6
f(f-1) = -5 - q
Since f(f-1) is divisible by x+1, we have:
f(f-1) = -5 - q = 0
Therefore, q = -5.
Hence, the value of q is -5 when f(fx) = x^3 + 2x^2 + qx - 6 is divisible by x+1.