The expression you provided is \( 3t^6 - 12t^5 \).

We can factor this expression by pulling out the greatest common factor (GCF) of the two terms. The GCF of \( 3t^6 \) and \( -12t^5 \) is \( 3t^5 \).

Factoring out \( 3t^5 \), we get:

\[
3t^6 - 12t^5 = 3t^5(t - 4)
\]

So, the factored form of the expression is:

\[
3t^5(t - 4)
\]

Would you like more details or have any questions about this? Here are some related questions:

1. How do you find the greatest common factor (GCF) of two terms?
2. Can this factored expression be simplified further?
3. What is factoring, and why is it useful in algebra?
4. How do you factor higher-order polynomials like \( t^6 \)?
5. What are some real-life applications of factoring polynomials?

**Tip**: Always start by looking for the greatest common factor when factoring an expression.

Learn how to factor the polynomial expression 3t^6 - 12t^5 by extracting the greatest common factor (GCF). This step-by-step solution demonstrates the application of algebraic factoring techniques and polynomials suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation