Question

which expressions are completely factored?
select each correct answer.

• $20x^3 + 12x^2 = 4x^2(5x + 3)$
• $18x^4 - 12x^2 = 6x(3x^3 - 2x)$
• $12x^5 + 8x^3 = 2x^3(6x^2 + 4)$
• $24x^6 - 18x^5 = 6x^5(4x - 3)$

Explanation:

Step1: Check first expression

Verify if $4x^2(5x+3)$ is fully factored:
The term $5x+3$ has no common factors, and $4x^2$ is the greatest common factor (GCF) of $20x^3$ and $12x^2$. This is completely factored.

Step2: Check second expression

Verify if $6x(3x^3-2x)$ is fully factored:
The term $3x^3-2x$ has a common factor of $x$, so it can be factored further to $6x \cdot x(3x^2-2)=6x^2(3x^2-2)$. This is not completely factored.

Step3: Check third expression

Verify if $2x^3(6x^2+4)$ is fully factored:
The term $6x^2+4$ has a common factor of $2$, so it can be factored further to $2x^3 \cdot 2(3x^2+2)=4x^3(3x^2+2)$. This is not completely factored.

Step4: Check fourth expression

Verify if $6x^5(4x-3)$ is fully factored:
The term $4x-3$ has no common factors, and $6x^5$ is the GCF of $24x^6$ and $18x^5$. This is completely factored.

Answer:

$\boldsymbol{20x^3 + 12x^2 = 4x^2 (5x + 3)}$
$\boldsymbol{24x^6 - 18x^5 = 6x^5 (4x - 3)}$