Question

What is the remainder when 8x³ 18x² 13x 9 is divided by 4x 3?

Answer 1

The remainder when 8x³ + 18x² + 13x + 9 is divided by 4x + 3 is 9.

Step-by-step explanation:

To find the remainder when 8x³ + 18x² + 13x + 9 is divided by 4x + 3, we can use the synthetic division method. Here are the steps:

1. Arrange the terms in descending order of powers of x: 8x³ + 18x² + 13x + 9
2. Set up the synthetic division table with 4x + 3 as the divisor:
3. Bring down the first coefficient, which is 8, into the first row of the table.
4. Multiply the divisor, 4x + 3, by the quotient of the previous division step, which is 2x² + 3x + 2, and write the result in the next row of the table:
5. Add the corresponding terms in each row:
6. The last number in the last row of the table (in this case, 9) is the remainder.

Therefore, the remainder when 8x³ + 18x² + 13x + 9 is divided by 4x + 3 is 9.