Question

Divide x² + 5x + 6 by x - 1 using synthetic division method?

Answer 1

To divide x² + 5x + 6 by x - 1, set up synthetic division with coefficients 1, 5, 6, and the root 1 from x - 1. Perform synthetic division to get the quotient polynomial x² + 6x + 12 with no remainder.

Step-by-step explanation:

To divide x² + 5x + 6 by x - 1 using the synthetic division method, we first identify the coefficient of each term in the dividend, which are 1, 5, and 6, respectively. Next, we write down the root of the divisor which is 1 (since x - 1 = 0 when x = 1), and set up our synthetic division table.

Using synthetic division:

1. Write the coefficients of the polynomial in a row: 1, 5, 6.
2. Write the root of the divisor on the left side: 1.
3. Bring down the first coefficient (1) to the bottom row.
4. Multiply the root by the number in the bottom row and write the result under the next coefficient (1 × 1 = 1).
5. Add the numbers in the second column (5 + 1 = 6).
6. Repeat the multiplication and addition steps until you reach the end of the row.

The synthetic division would look like this:

1 | 1 5 6
| 1 6
| 1 6 12
The bottom row now represents the coefficients of the quotient polynomial, which is x² + 6x + 12, and there is no remainder as the constant 6 is added to the last term of the quotient.