Question

Perform the division of the polynomial: (9x^3 − 19x^2 − 28x + 12) ÷ (x − 3) using synthetic division.

Answer 1

To perform division of a polynomial using synthetic division, arrange the terms in descending order of exponents and use a synthetic division table. The quotient is the coefficients in the remaining rows from left to right, and the remainder is the value in the last row.

Step-by-step explanation:

To perform the division of the polynomial (9x^3 − 19x^2 − 28x + 12) ÷ (x − 3) using synthetic division, follow these steps:

1. Arrange the terms of the polynomial in descending order of exponents.
2. Set up the synthetic division table by writing the divisor outside the table and bringing down the first coefficient of the dividend into the first row of the table.
3. Multiply the divisor by the value in the last row of the table and write the result under the next coefficient.
4. Add the values in the third row of the table and write the sum under the next coefficient.
5. Repeat steps 3 and 4 until all coefficients have been used.
6. The remainder is the value in the last row of the table.
7. The quotient is the coefficients in the remaining rows from left to right.

In this case, the quotient is 9x^2 + 8x - 4 and the remainder is 0.