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The Greatest Common Factor (GCF) is the highest number that divides exactly into two or more numbers. To determine the GCF, follow these steps:

1. **Factorize each term**: Break down each term into its prime factors. For example, in the polynomial \(-7p - 84\), the coefficients are \(-7\) and \(-84\).
2. **Identify common factors**: Find the prime factors that are common to both numbers. For \(-7\) and \(-84\), the common factor is \(-7\).
3. **Choose the highest common factor**: In this case, it is \(-7\), since that is the greatest factor present in both terms.

By factoring out this GCF from the given polynomial, we simplify the expression, making it easier to work with and understand.

Polynomials are algebraic expressions that consist of variables and coefficients, connected by addition, subtraction, or multiplication. They do not involve division by a variable. In the polynomial we are factoring, \(-7p - 84\), we have:

1. **Terms**: These are the separate parts of a polynomial, separated by a \(+\) or \(-\) sign. Here, \(-7p\) and \(-84\) are the terms.
2. **Coefficients**: These are the numerical parts of the terms that multiply the variables. For instance, \(-7\) is the coefficient of \(-7p\), and \(-84\) stands alone as a constant term.

Understanding the structure of polynomials is crucial for operations like addition, subtraction, multiplication, and especially factoring, as we are doing here.

Factoring involves breaking down an expression into simpler components, or factors, that multiply together to give the original expression. When factoring the greatest common factor out of a polynomial, follow these steps:

1. **Identify the GCF**: As we found earlier, the GCF of \(-7p\) and \(-84\) is \-7\.
2. **Divide each term by the GCF**: Doing this gives us the terms that, when multiplied by the GCF, return the original polynomial. For \(-7p\), dividing by \-7\ leaves us with \p\. For \(-84\), dividing by \-7\ leaves us with \12\.
3. **Rewrite the polynomial**: Combine these simplified terms, by placing them inside parentheses, and then multiply by the GCF: \-7(p + 12)\.

Through factoring, we convert a complex polynomial into a simpler, more manageable form.