Sure, I can help you understand the expression [tex]\( 3x^2 - 6x \)[/tex]. Let's break this down step by step.
### Step 1: Identify the Expression
The given expression is [tex]\( 3x^2 - 6x \)[/tex].
### Step 2: Recognize the Components
In this quadratic expression:
- The term [tex]\( 3x^2 \)[/tex] represents a quadratic term where the coefficient is 3.
- The term [tex]\( -6x \)[/tex] represents the linear term where the coefficient is -6.
### Step 3: Factoring the Expression
Next, we can factor the expression. Factoring involves expressing the given expression as a product of its simplest expressions. Here, both terms [tex]\( 3x^2 \)[/tex] and [tex]\( -6x \)[/tex] have a common factor of [tex]\( 3x \)[/tex].
1. Factor out the greatest common factor (GCF):
[tex]\[
\begin{align*}
3x^2 - 6x &= 3x (x - 2)
\end{align*}
\][/tex]
Thus, the expression [tex]\( 3x^2 - 6x \)[/tex] can be factored as [tex]\( 3x (x - 2) \)[/tex].
### Step 4: Double-Check the Factoring
To ensure the factoring is correct, you can expand the factored form back to the original expression:
[tex]\[
3x (x - 2) = 3x \cdot x - 3x \cdot 2 = 3x^2 - 6x
\][/tex]
This confirms the factored form is correct.
### Conclusion
The expression [tex]\( 3x^2 - 6x \)[/tex] can be factored to [tex]\( 3x (x - 2) \)[/tex].
