help please
Problem:
Use long division and the Remainder Theorem to evaluate , where
The quotient is
The remainder is
=
Divide $\displaystyle x^3- 5x^2+ 8x- 6$ by $\displaystyle x-2$
x divides into $\displaystyle x^3$ $\displaystyle x^2$ times and $\displaystyle x^3- 5x^2- x^2(x- 2)= x^3- x^3- 5x^2+ 2x^2= -3x^2$
so we now have $\displaystyle -3x^2+ 8x- 6$ left.
x divides into $\displaystyle -3x^2$ $\displaystyle -3x$ times and $\displaystyle -3x^2+ 8x- (-3x)(x-2)= -3x^+ 3x^2+ 8x- 6x= 2x$
so we now have $\displaystyle 2x- 6$ left.
x divides into $\displaystyle 2x- 6$ 2 times and $\displaystyle 2x- 6- 2(x-2)= 2x- 2x- 6+ 4= -2$
The quotient is $\displaystyle x^2- 3x+ 2$ and the remainder is -2.
(Check my arithmetic.)