Questions: Find the greatest common factor for the list of terms. x^5, x^7, x^8

Solution Steps

To find the greatest common factor (GCF) of the terms \(x^5\), \(x^7\), and \(x^8\), we need to identify the lowest power of \(x\) that is common to all terms. The GCF will be the term with the smallest exponent.

We are given the terms \(x^5\), \(x^7\), and \(x^8\).

The exponents of the terms are 5, 7, and 8.

To find the greatest common factor (GCF), we identify the minimum exponent among the given terms. The minimum exponent is: \[ \min(5, 7, 8) = 5 \]

The GCF of the terms is given by: \[ \text{GCF} = x^{\text{minimum exponent}} = x^5 \]

Final Answer