Answer :

The completely factored form of the expression 48x³ + 8x⁴ is: [tex]8x^3(6 + x)[/tex]

To factor the expression 48x³ + 8x⁴ completely, follow these steps:

  • Identify the Greatest Common Factor (GCF):

Look at the coefficients and variables in each term. The GCF of the coefficients 48 and 8 is 8. The smallest power of x in both terms is x³.

  • Factor out the GCF:

Pull out the GCF from each term.

[tex]48x^3 + 8x^4 = 8x^3(6 + x)[/tex]

  • Verify the factored expression:

Distribute the GCF back into the factored terms to ensure the original expression is obtained.

[tex]8x^3(6 + x) = 8x^3 \cdot 6 + 8x^3 \cdot x = 48x^3 + 8x^4[/tex]