Answer :

Certainly! Let's factor the expression [tex]\(48x^3 + 8x^4\)[/tex] step by step.

1. Identify a Common Factor:
- Look at both terms [tex]\(48x^3\)[/tex] and [tex]\(8x^4\)[/tex].
- Notice that both terms share a common factor. We can factor out the smallest constant and the lowest power of [tex]\(x\)[/tex].

2. Factor out the Greatest Common Factor (GCF):
- The GCF of the coefficients 48 and 8 is 8.
- The lowest power of [tex]\(x\)[/tex] found in both terms is [tex]\(x^3\)[/tex].
- So, the GCF is [tex]\(8x^3\)[/tex].

3. Factor the Expression:
- Divide each term by the GCF ([tex]\(8x^3\)[/tex]):
- For [tex]\(48x^3\)[/tex], divide by [tex]\(8x^3\)[/tex], resulting in [tex]\(6\)[/tex].
- For [tex]\(8x^4\)[/tex], divide by [tex]\(8x^3\)[/tex], resulting in [tex]\(x\)[/tex].
- Write the expression as a product of the GCF and the remaining terms:
[tex]\[
48x^3 + 8x^4 = 8x^3(6 + x)
\][/tex]

4. Final Factored Form:
- Therefore, the expression [tex]\(48x^3 + 8x^4\)[/tex] can be factored as [tex]\(8x^3(x + 6)\)[/tex].

That's the factored form of the expression!

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