Find the value of k for which the first polynomial is a factor of the second polynomial. x-1; -x^3 +4x^2+kx-2

Question

basic concepts and skills

Answer 1

Let P(x) = -x³ + 4x² + kx - 2

 

x-1 is a factor of P(x) if and only if P(1) = 0

 

P(1) = -1 + 4 + k - 2 = 0

 

                        1 + k = 0    So, k = -1.