Answer :

The result of dividing (-5x^3 - 8x^2 + 8) by (x + 2) using synthetic division is -5x^2 - 26x + 36 with a remainder of -64/(x + 2).

To perform synthetic division, we'll be dividing (-5x^3 - 8x^2 + 8) by (x + 2). The coefficients of the terms should be listed in descending order of powers of x, and the divisor should be written in the form (x - c), where c is the constant term.

The synthetic division process involves bringing down the leading coefficient, multiplying, and subtracting. Here's the setup:

-5 -8 0 8

_________________________

-2 | -5 -18 36 -72

|___________________

-5 -26 36 -64

The remainder is -64, and the quotient is -5x^2 - 26x + 36. Therefore, the result of the division is:

[tex]\[ \frac{-5x^3 - 8x^2 + 8}{x + 2} = -5x^2 - 26x + 36 - \frac{64}{x + 2} \][/tex]

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Rewritten by : Barada