Pregunta
factor. If the greatest common factor is 1, just retype the polynomial. \( 12 s^{4}+24 s^{3} \)
Ask by Patel Rojas. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The factored form of the polynomial \( 12s^{4} + 24s^{3} \) is \( 12s^{3}(s + 2) \).
Solución
To factor the polynomial \( 12s^{4} + 24s^{3} \), follow these steps:
1. **Find the Greatest Common Factor (GCF):**
- The coefficients are 12 and 24. The GCF of 12 and 24 is **12**.
- The variable parts are \( s^{4} \) and \( s^{3} \). The GCF is the lowest power, which is \( s^{3} \).
2. **Factor Out the GCF:**
\[
12s^{4} + 24s^{3} = 12s^{3}(s) + 12s^{3}(2) = 12s^{3}(s + 2)
\]
So, the factored form of the polynomial is:
\[
\boxed{12s^{3}(s + 2)}
\]
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Simplifique esta solución The Deep Dive
The greatest common factor (GCF) of \( 12s^{4} + 24s^{3} \) is \( 12s^{3} \). Factoring this out gives you \( 12s^{3}(s + 2) \). This means \( 12s^{4} + 24s^{3} \) can be simplified into a more manageable form, highlighting the structure of your polynomial. When factoring polynomials, always look for common factors first! A common mistake is to overlook smaller coefficients or variable powers. Set a checklist: identify the GCF, factor it out, and see if there's anything left to factor further. This approach can save you a lot of time and ensure you don’t miss potential factors!
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