Question

find the greatest common factor of the expressions.
30x⁵, 15x⁴

Explanation:

Step1: Find GCF of coefficients

The coefficients are 30 and 15. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The factors of 15 are 1, 3, 5, 15. The greatest common factor of 30 and 15 is 15.

Step2: Find GCF of variables

For the variable part \(x^5\) and \(x^4\), use the rule that the GCF of \(x^m\) and \(x^n\) (where \(m\geq n\)) is \(x^n\). Here, \(m = 5\) and \(n = 4\), so the GCF of \(x^5\) and \(x^4\) is \(x^4\).

Step3: Combine GCF of coefficients and variables

Multiply the GCF of the coefficients (15) and the GCF of the variables (\(x^4\)) to get the GCF of the two expressions. So, \(15\times x^4=15x^4\).

Answer:

\(15x^4\)