Factor the Expression: Breaking Down 2x³ + 4y⁴ + 8z⁵

In order solve the problem of factoring the following expression $2x^3 + 4y^4 + 8z^5$, we will identify and factor out the greatest common factor (GCF) from the terms. This process involves the following steps:

• Identify the coefficients of each term: The coefficients are 2 for $2x^3$, 4 for $4y^4$, and 8 for $8z^5$.

• Determine the GCF of the numbers 2, 4, and 8. The greatest common factor is 2.

• Factor out the GCF from each term in the expression:

Let's apply this step:

Initially, our expression is $2x^3 + 4y^4 + 8z^5$.

Factoring out the GCF of 2, we rewrite each term:

• $2x^3 = 2 \cdot x^3$

• $4y^4 = 2 \cdot 2y^4$

• $8z^5 = 2 \cdot 4z^5$

Thus, the expression becomes:

$2(x^3 + 2y^4 + 4z^5)$

We have successfully factored the expression by removing the GCF, 2, resulting in $2(x^3 + 2y^4 + 4z^5)$.

Therefore, the final factorized expression is $2(x^3 + 2y^4 + 4z^5)$.