Divide using synthetic division.
$$\frac{2x^5-2x^4+x^3-2x^2-2x-3}{x+2}$$
$$\frac{2x^5-2x^4+x^3-2x^2-2x-3}{x+2}=◻$$
(Simplify your answer.)

Step 1 ：Given the polynomial division problem $\frac{2x^5-2x^4+x^3-2x^2-2x-3}{x+2}$, we can solve it using synthetic division.

Step 2 ：First, we set up the synthetic division. The coefficients of the dividend (the polynomial we are dividing) are [2, -2, 1, -2, -2, -3]. The divisor is -2.

Step 3 ：We perform the synthetic division, which gives us the quotient [2, 2, 5, 8, 14, 25].

Step 4 ：This means that the quotient of the division is $2x^4+2x^3+5x^2+8x+14$ with a remainder of 25.

Step 5 ：Therefore, the division can be written as $2x^4+2x^3+5x^2+8x+14+\frac{25}{x+2}$.

Step 6 ：So, the solution to the given polynomial division problem is $\boxed{{\displaystyle 2x^4+2x^3+5x^2+8x+14+\frac{25}{x+2}}}$.