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-x2 - 2x - 4 which is B

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.

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