Question

PLEASE HELP ME!! It's a real struggle man

Which of the following expressions is this one equivalent to?

`(4x^(3)+2x^(2)+x+3)/(x+2)`


A.)
`4x^(3) -6x+13+(23)/(x+2)`

B.)
`4x^(2) -6x+13-(23)/(x+2)`

C.)
`4x-6+(13)/(x+2)`

D.)
`4x^(2) +13-(2)/(x+2)`

Answer 1

Option B.

Explanation:

The given expression is
`(4x^(3)+2x^(2)+x+3)/(x+2)`

Now we will divide the numerator by the given denominator.

x + 2 ) 4x³ + 2x² + x + 3 ( 4x² - 6x + 13

4x³ + 8x²

-6x² + x

-6x² -12 x

13x + 3

13x + 26

- 23

Therefore, remainder is (-23) and quotient is (4x² - 6x + 13) forms the expression as

4x³ - 6x + 13 -
`(23)/(x + 2)`

Option B. is the answer.