https://file.aiquickdraw.com/mathbot/file/1729540008021m599h5pe.jpg

The expression given in the image is:

\[
5g^5 + 15g^3 + g
\]

We need to factor out the greatest common factor (GCF). To do this:

1. **Identify the common factors in the coefficients:**
   - The coefficients are 5, 15, and 1 (since \(g\) can be written as \(1g\)).
   - The GCF of 5, 15, and 1 is 1 (since no number larger than 1 divides all of them).
   
2. **Identify the common powers of the variable \(g\):**
   - The powers of \(g\) are \(g^5\), \(g^3\), and \(g^1\).
   - The GCF of the powers is \(g^1\), because \(g\) is present in all terms, and the lowest exponent is 1.

So, the GCF of the entire expression is \(g\).

3. **Factor out \(g\) from each term:**
   - \(5g^5 \div g = 5g^4\)
   - \(15g^3 \div g = 15g^2\)
   - \(g \div g = 1\)

Thus, the factored form of the expression is:

\[
g(5g^4 + 15g^2 + 1)
\]

Would you like a further breakdown or explanation? Here are some related questions to deepen your understanding:

1. How do you determine the greatest common factor of polynomials?
2. What are the steps for factoring a polynomial completely?
3. How do you factor out variables from terms with different exponents?
4. How does factoring help in solving polynomial equations?
5. Can a polynomial with no common numerical factors still be factored using variables?

**Tip:** Always start by factoring out the greatest common factor before attempting more complex factorization methods.

Factor out the greatest common factor of the polynomial 5g^5 + 15g^3 + g.

Learn how to factor out the greatest common factor of the polynomial 5g^5 + 15g^3 + g. This tutorial breaks down the steps, including identifying the GCF and simplifying the expression. Suitable for students in Grades 8-10.

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