To divide the polynomial (-2z^3 - z + z^2 + 1) by (z + 1), polynomial long division is the recommended method. The process involves rearranging the polynomial in standard form, then dividing the leading term of the dividend by the leading term of the divisor. After obtaining the first term of the quotient, multiply the entire divisor by this term and subtract from the original polynomial. Repeat this process until reaching a remainder that is of lower degree than the divisor. Understanding polynomial long division is essential for successfully completing this division.