Question

a student used synthetic division to divide x^3-3x^2-2x by x+1
a. Describe and correct the error shown. (3 points)
b. Use the Remainder theorem to double check the remainder you found in part a. (2 points)

Answer 1

Answer:

The Synthetic Division and Remainder theorem is as shown below

Step-by-step explanation:

Given:

Polynomial $x^{3} -3x^{2} -2x$ divided by $x+1$

Solution:

For Synthetic Division we need to have coefficients,

So  the coefficients are

1, -3, 2, 0

and we have $x+1$

∴    -1   1   -3  2   0      

               -1   4   -6      

           1   -4  6  -6

Now the remainder is -6  by synthetic division

In Remainder theorem substitute $x=-1$ in the polynomial we will get the required remainder.

$(-1)^{3} -3(-1)^{2} -2(-1)$

∴ = -1 -3-2

∴ = -6

which is same as in synthetic division.