A student used synthetic division to divide x^3-x^2-2x by x+1 .

Question

This is what the students problem looked like
1_| 1 -1 -2
1 0
____________
1 0 -2
answer x remainder -2
a. Describe and correct the error shown.
b. Use the Remainder theorem to double check the remainder you found in part a.

Answer 1

I will attempt to line up the columns

-1_| 1 -1 -2 0 <---- there was no constant, so put in a zero
......... -1 2 0
__________
...... 1 -2 0 0

so (x^3-x^2-2x) by (x+1) = x^2 - 2x with zero remainder

check: f(-1) = (-1)^3 - (-1)^2 - 2(-1) = -1 - 1 + 2 = 0

double check:
(x+1)(x^2 - 2x)
= x^3 - 2x^2 + x^2 - 2x
= x^3 - x^2 - 2x , all checks out