Question

Find k so that x-1 is a factor of x^3 -3x^2 + kx - 1

Answer 1

By the remainder theorem, if p(x) = x³ - 3x² + kx - 1 and x - 1 is a factor p(x), then the remainder upon dividing p(x) by x - 1 is p (1) = 0.

So we have

p (1) = 1³ - 3 • 1² + k - 1 = 0

Solve for k :

1 - 3 + k - 1 = 0

k = 3