Question

Divide using synthetic division.

(x² −2x−8)÷(x+2)

(a) x−4
(b) x+4
(c) x−2
(d) x+2

Answer 1

Using synthetic division, the polynomial x² − 2x − 8 divided by x + 2 yields the quotient x - 4 with no remainder, making option (a) the correct answer.

Step-by-step explanation:

To divide the polynomial x² − 2x − 8 by x + 2 using synthetic division, we first note that the divisor x + 2 corresponds to the root x = -2. Here are the steps for synthetic division:

1. Write down the coefficients of the polynomial 1, -2, -8 for the terms x², x, and the constant term respectively.
2. Below the coefficients, write the root of the divisor, which is -2.
3. Carry down the leading coefficient to the bottom row.
4. Multiply this coefficient by -2 and write the result under the next coefficient.
5. Add the numbers in the second column to get the new coefficient.
6. Repeat the multiplication and addition process for the rest of the coefficients

After applying synthetic division, the resulting polynomial is the quotient, and the remainder (if any) is the last term in the bottom row. For this division, the quotient is x - 4 with no remainder, so the answer is option (a) x - 4.