91Ó°ÊÓ

The Greatest Common Factor (GCF) is the largest factor that can evenly divide all terms of a polynomial.
In our exercise, we have the polynomial \(2x^2 - 18\). We need to identify the GCF of the coefficients 2 and -18.
Since both numbers share the factor 2, it is the GCF.
Factoring out the GCF simplifies the polynomial by removing this factor from each term. For our polynomial, it turns into \(2(x^2 - 9)\).
This step is crucial because it makes the next steps of factoring much easier.

The difference of squares is a specific type of quadratic expression. It takes the form \(a^2 - b^2\).
This can always be factored into \((a+b)(a-b)\).
In our exercise, we reach the expression \(x^2 - 9\) after factoring out the GCF. Notice that this can be rewritten as \(x^2 - 3^2\), fitting the difference of squares format.
Applying the difference of squares rule, \(x^2 - 9\) becomes \((x+3)(x-3)\). This step exploits the structure of certain quadratics and offers a straightforward factoring method.

Quadratic expressions are polynomials that follow the form \(ax^2 + bx + c\). In many cases, they can be factored into products of linear binomials.
In our problem, once we factor out the GCF, we are left with \(x^2 - 9\), a simple quadratic with no linear term. This is a special case since it's also a difference of squares.
Generally, the approach involves: identifying patterns (like the difference of squares), factoring out the GCF first, and then breaking down the quadratic expression further.
For more complex quadratics, formulas such as the quadratic formula or completing the square might be used.
But in our exercise, recognizing the difference of squares allowed a simpler solution.