Answer :

Using synthetic division, we find that the value of th Quotient of 3x³-77x-19 X+5 is 3x²-15x+68.

To get the quotient, we use synthetic division. Follow these steps to find the quotient:

1: In the first row, write the coefficients of the polynomial being divided. 3 -77 0 -19

2: The second row starts with the divisor, (x+5), which is rewritten as -5 and placed in the leftmost box of the second row.

3: Bring down the first coefficient of the first row, which is 3 in this case. Write it in the third row next to the divisor.-5 3

4: To get the number in the next box, multiply -5 by 3 and write the product in the next box of the third row. That is -15.-5 3 -15

5: Add -77 and -15, write the sum in the fourth row under the second box, which is -92.-5 3 -15 -92

6: Multiply -5 and -92 to get 460 and write it in the last box of the third row.-5 3 -15 -92 460

7: Add the last two numbers, -19 and 460, and write the sum in the fourth row, under the third box, which is 441.-5 3 -15 -92 460 441

8: The final row contains the coefficients of the quotient. The first coefficient is 3, the second coefficient is -15, and the third coefficient is 68.

Therefore, the quotient is 3x²-15x+68.

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