Let's do the long division
color(white)(aaaa)aaaa2x^3-5x^2+4x-42x3−5x2+4x−4∣∣x-2x−2
color(white)(aaaa)aaaa2x^3-4x^22x3−4x2color(white)(aaaaaaaa)aaaaaaaa∣∣2x^2-x+22x2−x+2
color(white)(aaaaaa)aaaaaa0-x^2+4x0−x2+4x
color(white)(aaaaaaaa)aaaaaaaa-x^2+2x−x2+2x
color(white)(aaaaaaaaaaa)aaaaaaaaaaa0+2x-40+2x−4
color(white)(aaaaaaaaaaaaa)aaaaaaaaaaaaa+2x-4+2x−4
color(white)(aaaaaaaaaaaaaa)aaaaaaaaaaaaaa+0-0+0−0
so, the remainder is 00 and the quotient is 2x^2-x+22x2−x+2
You can also use the remainder theorem to see that the remainder is =0=0
If p(x)p(x) is a polynomial, and (x-a)(x−a) is a factor of that polynomial
Then, p(a)=(x-a)q(a)+0p(a)=(x−a)q(a)+0
q(a)q(a) is the quotient and 00 the remainder
Let f(x)=2x^3-5x^2+4x-4f(x)=2x3−5x2+4x−4
Then, f(2)=2*2^3-5*2^2+4*2-4f(2)=2⋅23−5⋅22+4⋅2−4
=16-20+8-4=24-24=0=16−20+8−4=24−24=0
The remainder is =0=0