Adding/Subtracting/Multiplying Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. 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. For example, $$(3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 2x + 5$$ .

Subtracting polynomials involves distributing the negative sign and then combining like terms. For example, $$(5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2$$ .

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, $$2x(3x^2 + 4x) = 6x^3 + 8x^2$$ .

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

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, while $$3x^2$$ and $$4x$$ are not.

The result is $$6x^2 + 3x + 5$$ .

The result is $$2x^2 - 2$$ .

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

The product is $$6x^3 - 10x^2$$ .