Question

Use synthetic division to divide

Answer 1

Answer: Please see attached images

(2nd image is the answer, 1st image is it worked out)

Explanation:

You are given "Use synthetic division to divide
`x^3 + 6x^2 +15x + 24` by
`x + 3`"

1) You first take the coefficients from the expression,
`x^3 + 6x^2 +15x + 24`, and place them in a row.

| 1 6 15 24

|__________________

2) Next you take the expression, x + 3, and take the last coefficient and put it to the left.

3 | 1 6 15 24

|__________________

3) Next you drop the 1 (this is the case for the first number of any synthetic division problem)

3 | 1 6 15 24

|__ ↓_______________

1

4) Now you multiply 3 and 1, then place that product under 6.

3 | 1 6 15 24

|__ ↓__ 3___________

1

5) Then you subtract the column: 6 - 3, and put the answer below

3 | 1 6 15 24

|__ ↓__ 3___________

1 3

6) Now you repeat this process (steps 4-5) but with the following numbers. So repeating step 4, You multiply 3 and 3, and put that product under 15.

3 | 1 6 15 24

|__ ↓__ 3__ 9________

1 3

7) Repeating step 5, you subtract the column: 15 - 9, and put the answer below.

3 | 1 6 15 24

|__ ↓__ 3__ 9________

1 3 6

8) Once again, you repeat steps 4-5. So repeating step 4, you multiply, 3 and 6, and you place the product under 24.

3 | 1 6 15 24

|__ ↓__ 3__ 9___18____

1 3 6

9) Repeat step 5, you subtract the column: 24 - 18, and put the answer below.

3 | 1 6 15 24

|__ ↓__ 3__ 9___18____

1 3 6 | 6

To find the quotient, that is result of the synthetic division but with its variables, and not including the remainder.

Quotient:
`x^2+3x+6`

The remainder is the remaining number that is at the bottom of the last column.

Remainder: 6