Question

determine if x^3-3x^2+4x-4 is indivisible by x-2

Answer 1

P(x) = x^3 - 3x^2 + 4x - 4

g(x) = x-2

On putting x = 2

P(2) = (2)^3 - 3(2)^2 + 4(2) - 4

=> P(2) = 8 - 12 + 8 - 4

=> P(2) = 16 - 16

=> P(2) = 0

=> g(x) is factor of p(x)

Answer 2

X-2)X^3-3X^2+4X-4 (X^2-X+2
+X^3-2X^2
___________________
- X^2+4X-4
-X^2+2X
____________________
2X-4
+2X-4
_____________________
0
______________________
Hence, x^3-3x^2+4x-4 is divisible by x-2