Question

Which statements are true?

Select each correct answer.



Responses

100x3+5=5x3(20x+1)
100 x cubed plus 5 equals 5 x cubed left parenthesis 20 x plus 1 right parenthesis

8x3−6x=2x3(4−3x3)
8 x cubed minus 6 x equals 2 x cubed left parenthesis 4 minus 3 x cubed right parenthesis

4x2+10x=2x(2x+5)
4 x squared plus 10 x equals 2 x left parenthesis 2 x plus 5 right parenthesis

30x4−12x3=6x3(5x−2)

Answer 1

Let's evaluate each statement one at a time.

1. **100x³ + 5 = 5x³(20x + 1)**

On the right side, we distribute:
- \(5x^3(20x + 1) = 100x^4 + 5x^3\)

So the left side does not equal the right side:
- **False**

2. **8x³ - 6x = 2x³(4 - 3x³)**

Again, we distribute on the right side:
- \(2x^3(4 - 3x^3) = 8x^3 - 6x^6\)

The left side does not equal the right side:
- **False**

3. **4x² + 10x = 2x(2x + 5)**

For this statement, we distribute on the right side:
- \(2x(2x + 5) = 4x^2 + 10x\)

The left side equals the right side:
- **True**

4. **30x⁴ - 12x³ = 6x³(5x - 2)**

We distribute on the right side:
- \(6x^3(5x - 2) = 30x^4 - 12x^3\)

The left side equals the right side:
- **True**

So the true statements are:

3) **4x² + 10x = 2x(2x + 5)**

4) **30x⁴ - 12x³ = 6x³(5x - 2)**