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Factoring is the process of breaking down an expression into a product of simpler expressions, called factors. It is an essential tool, especially when dealing with quadratic equations, such as the equation in our problem: \[x^2 - 3x = 0\].Factoring helps us simplify the equation and make it easier to solve. In many scenarios involving quadratic equations, factoring is the first step to finding the solution. Here, we used factoring to simplify our equation and make it easier to handle.When factoring quadratic expressions, we look for a pattern or a greatest common factor. In most straightforward cases, when an equation is in the form \(ax^2 + bx + c = 0\), we first find any common factors across all terms.

Solving equations is about finding the value of unknown variables that satisfy the equation. For quadratic equations like \[x^2 - 3x = 0\], solving starts with simplifying the equation through factoring.Once we have factored the equation into \[x(x - 3) = 0\], we express it as two separate equations. Each factor represents a potential solution to the original equation when set to zero. Thus, we get:

• \(x = 0\)
• \(x - 3 = 0\)

By solving these simpler equations,

• From \(x = 0\), we directly obtain \(x = 0\).
• For \(x - 3 = 0\), we add 3 to both sides to find \(x = 3\).

This method ensures that all potential solutions are considered.

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or terms exactly. Identifying the GCF is a critical step in the factoring process, as it simplifies expressions and prepares them for solving.In the equation \[x^2 - 3x = 0\],the terms have \(x\) in common. Here, \(x\) is the GCF. When we factor out \(x\), we rewrite the equation as \[x(x - 3) = 0\].This process of factoring out the GCF helps break down more complex expressions, allowing us to solve for the variable efficiently. By using the GCF, the equation becomes simpler, laying the groundwork for finding solutions quickly.