What is obtained after simplifying (x^2+x+x^2+x+1)?

(2x^2+2x+1)

Simplifying a polynomial means combining only like terms. Like terms have the same variables with the same powers, so their coefficients can be added. In the expression \(x^2+x+x^2+x+1\), the two \(x^2\) terms combine to give \(2x^2\). The two x terms combine to give \(2x\). The number 1 is a constant and has no matching constant, so it remains 1. Therefore the simplified expression is \(2x^2+2x+1\), which is option A.

A useful check is to group the terms: \((x^2+x^2)+(x+x)+1\). Adding each group gives \(2x^2+2x+1\). We must not multiply the terms or change their powers; addition combines coefficients of identical variable parts. Thus option B incorrectly changes the coefficient and loses the x term, while C and D use incorrect powers. The grouping confirms option A.

This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Algebraic expressions.