Question

Determine wheather (x-2) is a factor of x cube - 3x square + 4x - 4​

Answer 1

If (x-2) is a factor of the given polynomial, then we must get the value of the polynomial as 0, if we substitute 2 in place of x.

Let

$p(x) = x^3-3x^2+4x+4$

$p(2) = 2^3-3(2^2)+4(2)-4$

       $= 8 - 12+8-4$

       $= 16-16 = 0$

Hence (x-2) is a factor of the given polynomial

     

Answer 2

Answer:

x^2 - x + 2

Step-by-step explanation:

acco. to question

x^3 - 3x^2 + 4x - 4

take x-2 as a factor

x^2(x-2) - x^2 + 4x - 4

x^2(x-2) - x(x-2) + 2x - 4

x^2(x-2) - x(x-2) + 2(x-2)

(x^2 - x + 2) is the factor of

x^3 - 3x^2 + 4x -4