Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.50r2–2r

1. Break Down the Problem

We need to factor the given polynomial $50r^2 - 2r$ by identifying the greatest common factor (GCF) of the terms.

2. Relevant Concepts

The GCF of a polynomial is the largest factor that is common to each term in the polynomial. We will analyze both terms: $50r^2$ and $-2r$.

3. Analysis and Detail

1. Identify the coefficients:

   • The coefficient of the first term $50$ and the coefficient of the second term $-2$.
   • The GCF of $50$ and $-2$ is $2$.

2. Identify the variable part:

   • The first term has $r^2$ and the second term has $r$.
   • The GCF of $r^2$ and $r$ is $r$.

3. Combine the GCF:

   • Therefore, the GCF of the entire expression $50r^2 - 2r$ is $2r$.

4. Verify and Summarize

Now, we can factor out $2r$: $50r^2 - 2r = 2r(25r - 1)$

Final Answer

The polynomial factored is: $2r(25r - 1)$