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To find the greatest common divisor (GCD) of \(4x^2\) and \(30x^5\), let's break down the terms.

1. **Coefficients:**
   - The coefficient of \(4x^2\) is 4.
   - The coefficient of \(30x^5\) is 30.
   - The GCD of 4 and 30 is 2 (since 2 is the largest number that divides both 4 and 30).

2. **Variable Powers of \(x\):**
   - In \(4x^2\), the power of \(x\) is 2.
   - In \(30x^5\), the power of \(x\) is 5.
   - The GCD of \(x^2\) and \(x^5\) is \(x^2\) (since \(x^2\) is the highest power of \(x\) that divides both terms).

3. **Combine the GCD for Both Parts:**
   - Therefore, the GCD of \(4x^2\) and \(30x^5\) is \(2x^2\).

### Answer:
The greatest common divisor of \(4x^2\) and \(30x^5\) is \(2x^2\).

Would you like further details on this process or have any questions?

Here are 5 related questions for further practice:
1. What is the GCD of \(6x^3\) and \(18x^4\)?
2. How would you find the GCD of three terms, such as \(8x^4\), \(12x^2\), and \(16x^3\)?
3. What is the least common multiple (LCM) of \(4x^2\) and \(30x^5\)?
4. How do you find the GCD of polynomial expressions like \(4x^2 + 8x\) and \(12x^3 + 30x^2\)?
5. Can you find the GCD of \(5x^3\) and \(20x^7\)?

**Tip:** When finding the GCD of terms with variables, always take the lowest power of each variable.

halla el maximo comun divisor de 4x^2, 30x^5

Learn how to find the greatest common divisor (GCD) of 4x^2 and 30x^5 with step-by-step guidance. This example covers key algebraic concepts, including the GCD of coefficients and the lowest power of variables in common. Ideal for high school students in Grades 9-10.

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