Pregunta
Question 9 of 10 Find the common factor of all of the terms of the polynomial below \( 14 x^{2}-12 x \) A. \( 4 x \) B. \( 2 x^{2} \) C. \( 2 x \) D. \( 4 x^{2} \)
Ask by Bush Hart. in the United States
Feb 05,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The greatest common factor is \( 2x \).
Solución
To find the **greatest common factor (GCF)** of the polynomial \( 14x^{2} - 12x \), follow these steps:
1. **Factor Each Term:**
- \( 14x^{2} = 2 \times 7 \times x \times x \)
- \( -12x = -1 \times 2 \times 2 \times 3 \times x \)
2. **Identify Common Factors:**
- Both terms share the factors **2** and **x**.
3. **Determine the GCF:**
- Multiply the common factors: \( 2 \times x = 2x \).
So, the greatest common factor of the polynomial \( 14x^{2} - 12x \) is **\( 2x \)**.
**Answer:**
C. \( 2 x \)
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Simplifique esta solución Beyond the Answer
To find the common factor of the polynomial \( 14 x^{2}-12 x \), we can first identify the coefficients and the variables in each term. The greatest common factor of the numerical coefficients 14 and 12 is 2, and both terms share at least one factor of \( x \). Therefore, the overall common factor is \( 2x \). Looking at the options provided, the correct answer is \( C. 2 x \). To further illustrate, factoring out \( 2x \) from the polynomial yields: \[ 14x^2 - 12x = 2x(7x - 6) \] Now you can see how \( 2x \) effectively pulls the shared factor out of the polynomial, simplifying it nicely.
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