Question

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

Answer 1

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.