Question

find the value of k if x-1 is a factor of:
$4 {x}^{3} + 3 {x }^{2} - 4x + k$
​

Answer 1

x - 1 is a factor of 4x^3 + 3x^2 -4x +k

then x=1 is one root of 4x^3 + 3x^2 -4x +k

put x= 1

4x^3 +3x^2 -4x +k = 0

=> 4 (1)^3 +3 (1)^2-4 (1) +k =0

=> 4 + 3 - 4 + k = 0

=> k = -3

Answer 2

Answer:

$4 {x}^{3} + 3 {x}^{2} - 4x + k = 0 \\ \\ \\ x - 1 = 0 \\ \\ = > x = 1 \\ \\ \\ = 4 + 3 - 4 + k = 0 \\ \\ = > 7 - 4 + k = 0 \\ \\ = > 3 + k = 0 \\ \\ = > k = - 3$