Final answer:
Synthetic division is used to divide a polynomial by a binomial of the form (x - c) where c is a constant. The question involves dividing (2x^4 - 3x^3 - 6x^2 + 11x + 8) by (x - 2) using synthetic division to find the quotient and the remainder. The result would be a quotient and a remainder, which are obtained by the step-by-step synthetic division process.
Step-by-step explanation:
The question asks for the result of synthetic division with remainders when dividing (2x4 − 3x3 − 6x2 + 11x + 8) by (x − 2). To perform synthetic division, we follow these steps:
- Write down the coefficients of the polynomial: 2, -3, -6, 11, and 8.
- Write the zero of the divisor, which is the value that makes (x − 2) = 0, so here the zero is 2.
- Bring down the first coefficient (2) as it is.
- Multiply this coefficient by the zero (2) and write the result under the next coefficient (-3).
- Add these two numbers to find the new coefficient.
- Continue this process until all coefficients have been worked through.
- The final row will give the coefficients of the quotient and the remainder if there is any.
By doing this step-by-step, we would find the quotient of the division: (2x3 + x2 - 10x - 9) with a remainder of 10.