Question

find the greatest common factor of the expressions.
$5x^8$, $30x$

Explanation:

Step1: Find GCF of coefficients

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

Step2: Find GCF of variables

For the variable part, we have \(x^8\) and \(x\). Using the rule that the GCF of \(x^m\) and \(x^n\) (where \(m\geq n\)) is \(x^n\), here \(m = 8\) and \(n = 1\), so the GCF of \(x^8\) and \(x\) is \(x\).

Step3: Combine GCF of coefficients and variables

Multiply the GCF of the coefficients and the GCF of the variables. So \(5\times x=5x\).

Answer:

\(5x\)