Question

Which expressions are completely factored?

Select each correct answer.



Responses

18x4−12x2=6x(3x3−2x)
18 x begin power 4 end power minus 12 x squared equals 6 x left parenthesis 3 x cubed minus 2 x right parenthesis

20x3+12x2=4x2(5x+3)
20 x cubed plus 12 x squared equals 4 x squared left parenthesis 5 x plus 3 right parenthesis

12x5+8x3=2x3(6x2+4)
12 x begin power 5 end power plus 8 x cubed equals 2 x cubed left parenthesis 6 x squared plus 4 right parenthesis

24x6−18x5=6x5(4x−3)

Answer 1

To determine if the expressions are completely factored, we need to check if any further factoring can be done on the factored components.

1. **18x^4 - 12x^2 = 6x(3x^3 - 2x)**:
- The term \(3x^3 - 2x\) can be further factored as \(x(3x^2 - 2)\). Therefore, this expression is not completely factored.

2. **20x^3 + 12x^2 = 4x^2(5x + 3)**:
- The term \(5x + 3\) cannot be factored further. Thus, this expression is completely factored.

3. **12x^5 + 8x^3 = 2x^3(6x^2 + 4)**:
- The expression \(6x^2 + 4\) can be factored as \(2(3x^2 + 2)\). Thus, this expression is not completely factored.

4. **24x^6 - 18x^5 = 6x^5(4x - 3)**:
- The term \(4x - 3\) cannot be factored further. Thus, this expression is completely factored.

Based on this analysis, the completely factored expressions are:

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