Add or subtract, as indicated. See Example 2. (5x^2-4x+7) + (-4x^2+3x-5)

Verified step by step guidance

1. Identify the like terms in the polynomials: terms with the same degree of x.
2. Combine the coefficients of the like terms for the x^2 terms: 5x^2 and -4x^2.
3. Combine the coefficients of the like terms for the x terms: -4x and 3x.
4. Combine the constant terms: 7 and -5.
5. Write the resulting polynomial by combining all the simplified terms.

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 (5x^2 - 4x + 7) + (-4x^2 + 3x - 5), you would add the coefficients of x^2, x, and the constant terms separately to simplify the expression.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. For instance, in the expression 5x^2 and -4x^2 are like terms because they both contain x raised to the power of 2. Identifying and combining like terms is essential for simplifying polynomial expressions accurately.

Combining Polynomials

Combining polynomials requires careful attention to the signs and coefficients of each term. When adding or subtracting polynomials, it is crucial to distribute any negative signs correctly and ensure that all like terms are accounted for. This process leads to a simplified polynomial that represents the sum or difference of the original expressions.