Question

Identify the correct factorization

10x^3+25x


Responses

5x(2x2+5)
5 x open paren 2 x squared plus 5 close paren

5x2(2x+5)
5 x squared open paren 2 x plus 5 close paren

10x(x2+25x)
10 x open paren x squared plus 25 x close paren

2x(5x2+10)

Answer 1

To factor the expression \(10x^3 + 25x\), we can start by finding the greatest common factor (GCF) of the terms in the expression.

1. **Identify the GCF:**
- The coefficients are 10 and 25, and their GCF is 5.
- The variable parts have \(x^3\) and \(x\), and the GCF is \(x\).
- Therefore, the GCF of the entire expression is \(5x\).

2. **Factor out the GCF:**
\[
10x^3 + 25x = 5x(2x^2 + 5)
\]

Now let's compare this with the provided responses:

1. **Response 1:** \(5x(2x^2 + 5)\) - **This is correct.**
2. **Response 2:** \(5x^2(2x + 5)\) - Incorrect.
3. **Response 3:** \(10x(x^2 + 25x)\) - Incorrect.
4. **Response 4:** \(2x(5x^2 + 10)\) - Incorrect.

Therefore, the correct factorization is **Response 1**: \(5x(2x^2 + 5)\).