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]
