Add, Subtract, Multiply Polynomials

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, $$2x^2 + 3x + 5$$ is a polynomial.

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms.

Combine like terms: $$(3x^2 + 5x^2) + (4x + 2x) = 8x^2 + 6x$$ .

Change the signs of the second polynomial and combine like terms: $$(6x^3 - 4x^3) + (2x - 3x) = 2x^3 - x$$ .

The degree of a polynomial is the highest power of the variable in the expression. For example, in $$4x^3 + 2x^2 + 5$$ , the degree is 3.

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in $$5x^4 + 3x^2 + 2$$ , the leading coefficient is 5.

Use the distributive property (FOIL): $$x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$ .

Multiply the coefficients and add the exponents: $$6x^3$$ .