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Which of the following expression is equivalent to x³+1/x+1.A) x²+xB) x²C) x²+1D) x²-x+1

User Raw Hasan
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1 Answer

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To answer whis question we have to remember the factorization of sum of cubes


x^3+y^3=(x+y)(x^2-xy+y^2)

In this case y=1, then


\begin{gathered} x^3+1=x^3+1^3 \\ =(x+1)(x^2-1\cdot x+1^2) \\ =(x+1)(x^2-x+1) \end{gathered}

So that


\begin{gathered} (x^3+1)/(x+1)=((x+1)(x^2-x+1))/(x+1) \\ =x^2-x+1 \end{gathered}

Therefore the answer is D.

User Nico Serrano
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