Question

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

Answer 1

k = 3

Explanation:

If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.

f (x ) = x³ - 3x² + Kx - 1 , then

plug 1 as x in the expression.

• f ( 1) = ( 1)³ - 3 ( 1)² + k (1) - 1 = 0

expand exponents

• 1 - 3 + k - 1 = 0

combine like terms

• -3 + k = 0

Add 3 to both side

• k = 3

Answer 2

`{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^(3) - {3x}^(2) + kx - 1}} \\ { \tt{f(1) : {(1)}^(3) - 3 {(1)}^(2) + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}`