Perform the indicated operations. (2x^2-x)+(x^2+4x)

Key Concepts

Polynomial Addition

Polynomial addition involves combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. For example, in the expression (2x^2 - x) + (x^2 + 4x), the like terms are 2x^2 and x^2, as well as -x and 4x. The result is a new polynomial formed by summing the coefficients of these like terms.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. Identifying like terms is crucial for simplifying expressions and performing operations such as addition or subtraction. In the expression given, 2x^2 and x^2 are like terms, while -x and 4x are also like terms. Combining these terms correctly is essential for obtaining the correct result.

Combining Coefficients

Combining coefficients is the process of adding or subtracting the numerical factors of like terms in a polynomial. When performing operations on polynomials, it is important to add the coefficients of like terms to simplify the expression. For instance, in the operation (2x^2 + x^2), the coefficients 2 and 1 are combined to yield 3, resulting in 3x^2 in the final expression.