Question

What is the remainder when (3x4 + 2x3 − x2 + 2x − 9) ÷ (x + 2)?

Answer 1

15

There you go.

Answer 2

ANSWER

The remainder is 15.



Step-by-step explanation

The given polynomial function is


`p(x) = 3 {x}^(4) + 2 {x}^(3) - {x}^(2) + 2x - 9`

We want to find the remainder when the given polynomial function is divided by


`x + 2`



According to the Remainder Theorem, if


`p(x) = 3 {x}^(4) + 2 {x}^(3) - {x}^(2) + 2x - 9`

is divided by


`x + 2`


Then the remainder is


`p( - 2)`


This means that, we have to substitute


`x = - 2`
into the given polynomial function and evaluate.


Thus,


`p( - 2) = 3 {( - 2)}^(4) + 2 {( - 2)}^(3) - {( - 2)}^(2) + 2( - 2)- 9`




`p( - 2) = 3 {( 16)} + 2 {( - 8)} - {( 4)} + 2( - 2)- 9`



`p( - 2) = 48 - 16- 4 - 4- 9`



`p( - 2) = 15`

Therefore the remainder is 15