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The Greatest Common Factor (GCF) is an essential concept in algebra that helps simplify expressions. It represents the largest factor that divides two or more numbers or terms without a remainder. When dealing with polynomials, finding the GCF means identifying a number or expression that can be evenly divided from each term in the polynomial.

Here's how you can approach it:

• List all the factors of each term. For coefficients, list their numerical factors. For variables, consider their powers.
• Identify any common factors between the terms.
• The GCF is the highest of these common factors.

In the polynomial expressed in the given problem, the terms are 7s² and 9t². However, these coefficients are co-prime (7 and 9 have no common factors other than 1), and the variables s and t are different. Therefore, there is no GCF other than 1 that can be applied, leaving the polynomial factored as itself.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (like addition, subtraction, multiplication, and division). They are building blocks in algebra used to represent real-world problems and abstract mathematics.

In algebra:

• Variables are symbols (like x, y, or in our exercise, s and t) used to represent unknown values.
• Coefficients are the numerical part assigned to variables. In the expression 7s², 7 is the coefficient.
• An expression can contain multiple terms separated by '+' or '-' signs.

Factoring such expressions means rewriting them as a product of simpler terms. In some cases, expressions can be factorable into polynomials with a common factor. However, as seen in our problem, if no GCF or similar terms exist across the expression, the expression remains unchanged.

A monomial is one of the simplest forms of an algebraic expression. It consists of a single term which can be a constant, a variable, or a product of constants and variables. Monomials do not involve addition or subtraction operations between different terms.

Characteristics of monomials include:

• They have only one term, such as 7s² or 9t².
• The term can include variables raised to any power, but never a negative or fractional exponent.
• They can be multiplied together, which results in another monomial. For instance, multiplying 3x by 4y gives 12xy.

When factoring polynomials, if the expression consists of several terms, one potential method is to identify if any monomial can serve as a common factor. In our example, 7s² and 9t² are each monomials, but they share no common monomial factor, so they cannot be combined further.