Answer: To find the common factors of 28x^3 and 20x^5, we need to identify the factors that both terms share.
First, let's break down the given terms into their prime factors:
- For 28x^3: 28 = 2 * 2 * 7, and x^3 represents x * x * x.
- For 20x^5: 20 = 2 * 2 * 5, and x^5 represents x * x * x * x * x.
Now, let's compare the prime factors:
- Both terms have two factors of 2 in common: 2 * 2.
- Both terms have x^3 in common, as they both have three factors of x: x * x * x.
To find the common factor, we multiply the common factors of the coefficients (2 * 2) and the common factors of the variables (x^3).
Therefore, the common factor of 28x^3 and 20x^5 is 4x^3.
Remember, when finding common factors, we look for the highest power of each common prime factor. In this case, 2^2 is the highest power of 2, and x^3 is the highest power of x that both terms share.
Explanation: