Final answer:
To factor the expression 4x^4 + 12x^3 + 8x, we identify and factor out the GCF, which is 4x. The expression becomes 4x(x^3 + 3x^2 + 2).
Step-by-step explanation:
The student's question asks us to factor the algebraic expression 4x⁴ + 12x³ + 8x by using the Greatest Common Factor (GCF).
To proceed with factoring, we need to determine the GCF of the coefficients and the variable terms.
All terms contain at least one factor of 4 and at least one x, so we can confidently factor out 4x from each term.
Here's the step-by-step factoring process:
Identify the GCF of the coefficients; here, it is 4.
Look for the lowest power of x present in all terms; which is x.
Factor out the GCF from each term: 4x is factored out.
Rewrite the original expression as a product of the GCF and the remaining terms: 4x⁴ + 12x³ + 8x becomes
4x(x³ + 3x² + 2).
In factored form, the expression is 4x(x³ + 3x² + 2).