Factor the expression $7x^2 - 35x$ completely, factoring out the greatest common factor.

1. Problem Description

Factor the expression $7x^2 - 35x$ completely, factoring out the greatest common factor.

2. Solution Steps

The given expression is $7x^2 - 35x$.

We look for the greatest common factor (GCF) of the coefficients and the variables.

The coefficients are 7 and -

3

5. The GCF of 7 and 35 is

7. The variables are $x^2$ and $x$. The GCF of $x^2$ and $x$ is $x$.

Therefore, the GCF of the entire expression is $7x$.

We factor out $7x$ from each term:

$7x^2 - 35x = 7x(x) - 7x(5) = 7x(x-5)$.

3. Final Answer

$7x(x-5)$