LF-ASSESSMENT 6. Divide (a)(x^3-3x^2-7x+6)div (x-2) and (b)(2x^3-16x+6)div (x+3) using synthetic division nolvnomials closed under division? Justify your answer.

To divide the given polynomials using synthetic division, we will follow the steps below:(a) Step 1: Write down the coefficients of the dividend polynomial: .Step 2: Write down the zero of the divisor polynomial, which is .Step 3: Bring down the first coefficient, which is .Step 4: Multiply the zero of the divisor by the value just brought down, and write the result under the next coefficient.Step 5: Add the values in the second column and write the result below the line.Step 6: Repeat steps 4 and 5 until all coefficients have been processed.The synthetic division table for this problem is as follows:``` 2 | 1 -3 -7 6 | 2 -2 -18 ---------------- 1 -1 -9 -12```The quotient is and the remainder is .(b) Step 1: Write down the coefficients of the dividend polynomial: .Step 2: Write down the zero of the divisor polynomial, which is .Step 3: Bring down the first coefficient, which is .Step 4: Multiply the zero of the divisor by the value just brought down, and write the result under the next coefficient.Step 5: Add the values in the second column and write the result below the line.Step 6: Repeat steps 4 and 5 until all coefficients have been processed.The synthetic division table for this problem is as follows:``` -3 | 2 0 -16 6 | -6 18 -6 ---------------- 2 -6 2 0```The quotient is and the remainder is .Therefore, the answers are:(a) (b) Polynomials are closed under division, meaning that the division of two polynomials always results in another polynomial. In this case, both and resulted in polynomials as the quotients.