## Answer :

1.

**Identify the common factors:**

First, we observe that both terms in the expression [tex]\(8 p x^3\)[/tex] and [tex]\(12 p x^2\)[/tex] share common factors:

- Both terms have the variable [tex]\(p\)[/tex].

- Both terms have the variable [tex]\(x\)[/tex], specifically with powers [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex].

- Both terms are divisible by 4.

2.

**Factor out the greatest common factor (GCF):**

The GCF for the numerical coefficients 8 and 12 is 4. Both terms contain [tex]\(p\)[/tex] and [tex]\(x^2\)[/tex] as the highest common power of [tex]\(x\)[/tex]. Thus, the GCF is [tex]\(4 p x^2\)[/tex].

[tex]\[ 4 p x^2 \times \left(\frac{8 p x^3}{4 p x^2} + \frac{12 p x^2}{4 p x^2}\right) \][/tex]

3.

**Simplify inside the parentheses:**

Simplify the terms inside the parentheses after factoring out [tex]\(4 p x^2\)[/tex]:

[tex]\[ 4 p x^2 \left(2 x + 3\right) \][/tex]

4.

**Combine the terms:**

Write the final, factorized form:

[tex]\[ 4 p x^2 (2 x + 3) \][/tex]

So, the expression [tex]\(8 p x^3 + 12 p x^2\)[/tex] factorizes to:

[tex]\[ 4 p x^2 (2 x + 3) \][/tex]

This is our final, fully factorized expression.