https://file.aiquickdraw.com/mathbot/file/172594154179588wufjlv.jpg

The problem asks to find the greatest common factor (GCF) for the given list of terms: \( y^4 \), \( y^3 \), and \( y^6 \).

To find the GCF of powers of the same variable, we need to identify the smallest exponent among the terms. In this case, the exponents of \( y \) are:

- \( y^4 \) has an exponent of 4,
- \( y^3 \) has an exponent of 3,
- \( y^6 \) has an exponent of 6.

The smallest exponent is 3, so the GCF is \( y^3 \), not just \( y \) (which would be \( y^1 \)).

It looks like the given answer in the screenshot is \( y \), but the correct GCF should be \( y^3 \).

Would you like more details or further clarification on this?

Here are 5 related questions to deepen your understanding:

1. How do you find the GCF of more complex algebraic terms involving multiple variables?
2. What happens if one of the terms has a coefficient (e.g., \( 2y^3 \))? How does that affect the GCF?
3. How would you find the GCF of three polynomials?
4. What is the GCF of terms that involve negative exponents, like \( y^{-2}, y^3, y^5 \)?
5. Can you explain why the smallest exponent determines the GCF?

**Tip:** When finding the GCF for powers of the same variable, always pick the variable with the smallest exponent as the common factor!

Find the GCF for the given list: y^4, y^3, y^6.

Discover how to find the greatest common factor (GCF) of the terms y^4, y^3, and y^6 by selecting the variable with the smallest exponent. This algebra problem covers concepts related to exponents and common factors. Suitable for high school students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation