Answer :

Final answer:

The result of performing synthetic division with divisor -1 and dividend coefficients 2, 8, 6 is: Quotient: -2x^2 - 10x - 4, Remainder: 0.

Explanation:

To perform synthetic division, arrange the coefficients of the dividend polynomial (2, 8, 6) and the divisor (-1). Start by bringing down the first coefficient, which is 2. Multiply the divisor, -1, by this value to get -2, and write it beneath the next coefficient, 8. Add these values to get 6. Multiply the divisor by 6 to get -6, write it beneath the last coefficient, 6, and the sum is 0. The result is the quotient -2x^2 - 10x - 4 with a remainder of 0.

Synthetic division is a method used to divide polynomials efficiently by linear binomials. In this case, -1 is the divisor, and the dividend coefficients are 2, 8, and 6. The process involves carrying out multiplication and addition iteratively to find the quotient and remainder. Each step involves multiplying the divisor by the current result and adding the next coefficient until the process is completed. The final result obtained, -2x^2 - 10x - 4, represents the quotient of the division, and the remainder is 0, indicating a perfect division without any remainder.

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Rewritten by : Barada