If (x-1),(x+1) and (x-2) are factors of the polynomial ax^3+bx^2+cx-1.

Question

Find a,b and c respectively?

Answer 1

Let f(x) = ax^3 + bx^2 + cx - 1.
If (x - p) is a factor of f(x), then f(p) = 0.

Since (x-1) is a factor of f(x), then f(1) = 0
f(1) = a(1)^3 + b(1)^2 + c(1) - 1 = 0
a + b + c - 1 = 0..........Equation 1

Repeat this process for (x + 1) and (x - 2), respectively, to get:
-a + b - c - 1 = 0..........Equation 2
8a + 4b + 2c - 1 = 0.........Equation 3

Solve this system of 3 equations in 3 unknowns to find a, b, and c.