Show whether she is right or wrong using long (or synthetic) division.

Question

Your classmate claims that (𝑥 + 2) is a factor of the polynomial 5𝑥³ +10𝑥³− 𝑥 − 2.

Answer 1

(5x³ + 10x² - x -2) ÷ (x + 2)

Using synthetic division will be more efficient.

-2| 5 10 -1 -2

____-10__0__2_____

5 0 -1 0

1) Bring the 5 down.

2) Multiply 5 by -2 to get -10 and put it under the 10.

3) Add 10 and -10 to get 0.

4) Repeat the same process until you hit the remainder.

Answer: 5x² - 1 with (x + 2) being a factor.