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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)

1 answer

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: \(5x(2x^2 + 5)\).