Question

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

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:

$Q=(x^3+8)\div(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know the following algebraic formula:

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

So, we have

$x^3+8\\\\=x^3+2^3\\\\=(x+2)(x^2-x\times2+2^2)\\\\=(x+2)(x^2-2x+4).$

Therefore, from equation (i), we have

$Q\\\\=(x^3+8)\div(x+2)\\\\\\=\dfrac{x^3+8}{x+2}\\\\\\=\dfrac{(x+2)(x^2-2x+4)}{(x+2)}\\\\=x^2-2x+4.$

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

Option (B) is correct.