Question

What is the quotient (x3 + 8) ÷ (x + 2)?

A x2 + 2x + 4
B x2 – 2x + 4
C x2 + 4
D x2 – 4

Answer 1

-x2 - 2x - 4 which is B

Answer 2

Answer: The correct option is (B)
`x^2-2x+4.`

Step-by-step explanation: We are given to find the following quotient:

`Q=(x^3+8)/(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know the following algebraic formula:

`x^3+a^3=(x+a)(x^2-ax+a^2).`

So, we have

`x^3+8\\\\=x^3+2^3\\\\=(x+2)(x^2-x*2+2^2)\\\\=(x+2)(x^2-2x+4).`

Therefore, from equation (i), we have

`Q\\\\=(x^3+8)/(x+2)\\\\\\=(x^3+8)/(x+2)\\\\\\=((x+2)(x^2-2x+4))/((x+2))\\\\=x^2-2x+4.`

Thus, the required quotient is
`x^2-2x+4.`

Option (B) is correct.