Simple maths question lower grade

Question

f(x) = 2x^3-8x^2+13x-10 / x^3-4x^2+5x-2 

apply long division to write the function in asymptotic form 

working out please

Answer 1

f (x ) = (2x ³ - 8x ² + 13x - 10) / (x ³ - 4x ² + 5x - 2)

x ³ - 4x ² + 5x - 2 ) 2x ³ - 8x ² + 13x - 10 (2

                                2x ³ - 8x ² + 10x - 4

                            (-)      (+)      (-)      (+)

                       ______________________________

                                           3x - 6

Quotient is 2 and remainder is 3x - 6.

f (x ) = (2x³ - 8x ² + 13x - 10) / (x ³ - 4x ² + 5x - 2)

f (x) = (x - 2)(2x ² - 4x + 5)/(x - 2)(x - 1) ²

f (x) = (2x ² - 4x + 5)/(x - 1)²

Asympototic form is f (x ) = 2 + [(3x - 6)/(x ³ - 4x ² + 5x - 2)].

or

f (x ) = 2 + [3/(x -1)²]