Question

please help!!!

Using long division, what is the quotient of this expression?
3x42x³-x-4
x²+2
OA. 3x²
3x - 4
OB. 3x² + 2x + x² + 2
O C.
3x² 2x
O D.
-
2x
3x² + 2x
- 6 +
-
- 5+
-
3x + 8
x² + 2
-
3x+6
x²+2
5x8
x² + 2
Rese

Answer 1

Check the picture below.

notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.

Answer 2

Here is the solution process:

                     3 x² -  2 x  -   6                      

x² + 0x + 2 | 3 x⁴ -  2 x³ +  0  x² -     x -   4

                    3  x⁴ + 0 x³ +  6  x²                

                             - 2 x³  -  6  x² -      x -   4

                             - 2 x³  + 0  x² -   4 x        

                                        -  6  x² +  3 x  -  4

                                        -  6  x²  + 0 x  -  12

                                                        3 x  + 8

Long division:

• Standard: $\sf{3x^{2} -2x-6+\dfrac{3x+8}{x^{2} +2} \ \ \to \ \ \ Option \ "A" }$
• Quotient: 3x² - 2x - 6
• Rest: 8 + 3x

Therefore, the correct option is "A".