Consider the polynomial function f(x)=3x^3-2x^2+kx-3 Find the value of k if (x - 1) is a factor of f(x).

Answer 1

use long division, dividing x-1 into 3x^3-2x^2 -kx -3 to get

3x^2 +x +-3 where k=2

(3x^2+x+3)(x-1) = 3x^3-2x^2+2x -3

x-1 is the only real factor

the other 2 factors are imaginary

Answer 2

3 -2 k -3

1 3 1 k + 1

--------------------------

3 1 k+1 0

-3 + k + 1 = 0 --> k = 2