Learn how to add polynomial expressions by combining like terms. Examples include (4x^2 + 5x + 7) + (3x^2 - 8x + 12).

Understand how to subtract polynomial expressions by distributing the negative sign to all terms in the second polynomial before combining like terms. Examples include (9x^2 - 7x + 13) - (5x^2 - 7x - 14).

Further practice subtracting polynomials, emphasizing careful distribution of the negative sign and combining like terms, even with terms of different powers. Example: (3x^3 - 5x + 8) - (7x^2 - 6x + 9).

Learn to subtract polynomials when there are coefficients outside the parentheses. Distribute the coefficients first, then combine like terms: 4(3x^2 + 6x - 8) - 3(2x^2 - 5x + 7).

Discover how to multiply two binomials using the FOIL method (First, Outer, Inner, Last). An example is (3x + 5) * (2x - 3).

Learn to simplify expressions like (2x - 5)^2 by writing it as two binomials multiplied together and then using the FOIL method.

Explore how to multiply a binomial by a trinomial, noting that the initial multiplication will result in six terms before combining like terms. Example: (4x - 2)(x^2 + 3x - 5).

Understand the process of multiplying two trinomials, which initially yields nine terms before combining like terms. Example: (3x^2 - 5x + 7)(2x^2 + 6x - 4).

Learn the first method for dividing polynomials: factoring. Factor the numerator and cancel common terms with the denominator. Example: (x^2 + 7x + 12) / (x + 3).

Understand how to divide polynomials using the long division method, step-by-step. Example: (2x^2 - x + 6) / (x - 2).

Learn the synthetic division method for dividing polynomials, focusing on setting up the problem and performing the calculations. Example: (2x^2 - 7x + 6) / (x - 2).