Question

PLEASE HELP ME!! It's a real struggle man
Which of the following expressions is this one equivalent to?
$\frac{4x^{3}+2x^{2}+x+3}{x+2}$


A.) $4x^{3} -6x+13+\frac{23}{x+2}$

B.) $4x^{2} -6x+13-\frac{23}{x+2}$

C.) $4x-6+\frac{13}{x+2}$

D.) $4x^{2} +13-\frac{2}{x+2}$

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given expression is $\frac{4x^{3}+2x^{2}+x+3}{x+2}$

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 - $\frac{23}{x + 2}$

Option B. is the answer.