Adding and Subtracting Polynomials

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x + 1 is a polynomial.

Adding polynomials involves combining like terms from two or more polynomial expressions. Like terms have the same variable raised to the same power.

Like terms are terms in a polynomial that have the same variable raised to the same exponent. For example, 2x^2 and 3x^2 are like terms.

Combine like terms: (3x^2 + 2x + 1) + (2x^2 - 4x - 5) = (3x^2 + 2x^2) + (2x - 4x) + (1 - 5) = 5x^2 - 2x - 4.

Combine like terms: (3x^3 + x^3) + (3x^2 - 2x^2) + (-4x + x) + (5 - 4) = 4x^3 + 1x^2 - 3x + 1.

The perimeter is the sum of the lengths of all sides. If the sides are represented by polynomials, add them together.

To subtract polynomials, change the sign of the polynomial being subtracted and then combine like terms.

Change the sign of the second polynomial: (a^2 - 3a - 4) - (2a^2 + 5a + 3) = a^2 - 3a - 4 - 2a^2 - 5a - 3 = -a^2 - 8a - 7.

Combine like terms: (2x + 3x) + (5y - 2y) = 5x + 3y.

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.