(1 point) Use synthetic division to find the quotient and remainder of $\frac{-2 x^{3}+2 x+1}{x+2}$ - Quotient: $\square$ help (formulas) - Remainder: $\square$ help (formulas) Note: You can earn partial credit on this problem.

Step 1 ：Write down the coefficients of the polynomial we are dividing, which are -2, 0 (since there is no \(x^2\) term), 2, and 1. Also write down the root of the divisor, which is -2 (since \(x + 2 = 0\) when \(x = -2\)).

Step 2 ：Set up the synthetic division table as follows: \[-2 | -2 0 2 1\]

Step 3 ：Perform the synthetic division: \[-2 | -2 0 2 1\] \[ | 4 -8 16\] \[-----------------\] \[ | -2 4 -6 17\]

Step 4 ：The numbers on the bottom row are the coefficients of the quotient and the remainder. The quotient is \(-2x^2 + 4x - 6\), and the remainder is 17.

Step 5 ：So, the quotient is \(-2x^2 + 4x - 6\) and the remainder is 17.