Answer :

We start with the expression

[tex]$$19x^3 - 38x^2.$$[/tex]

Step 1. Identify the Greatest Common Factor (GCF):

- Both terms have a numerical factor that can be divided by 19.
- Both terms also include a variable factor of at least [tex]$x^2$[/tex].

Thus, the GCF is

[tex]$$19x^2.$$[/tex]

Step 2. Factor out the GCF:

Divide each term by [tex]$19x^2$[/tex]:

- For the first term:

[tex]$$\frac{19x^3}{19x^2} = x.$$[/tex]

- For the second term:

[tex]$$\frac{-38x^2}{19x^2} = -2.$$[/tex]

Step 3. Write the factored form:

After factoring out the GCF, the expression becomes

[tex]$$19x^2(x - 2).$$[/tex]

Final Answer:

[tex]$$19x^2(x - 2).$$[/tex]

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