Question

Katniss divided x^3+2x^2-3x-4 by x+1. she didnt get a remainder. do you agree with her?

Answer 1

Katnis is right

Step-by-step explanation

We use the Remainder Theorem to check if she is right.

According to the Remainder Theorem, if the polynomial function,

`p(x) = {x}^(3) + 2 {x}^(2) - 3x - 4`

is divided by x+1, then the remainder is given by

`p( - 1)`

We substitute x=-1 into the function to obtain,

`p( - 1) = {( - 1)}^(3) + 2 { ( - 1)}^(2) - 3( - 1) - 4`

We simplify to get:

`p( - 1) = - 1+ 2 (1) + 3 - 4`

`p( - 1) = 4- 4`

`p( - 1) = 0`

Katnis is right because the remainder is zero