Math Problem Statement

z^9+z^6

Solution

The given expression is:

z9+z6z^9 + z^6

This is a sum of two terms, both involving powers of zz. To simplify or factor this expression, we can factor out the common term, which is the smallest power of zz, namely z6z^6:

z9+z6=z6(z3+1)z^9 + z^6 = z^6(z^3 + 1)

So, the factored form of the expression is:

z6(z3+1)z^6(z^3 + 1)

Would you like me to explore further aspects of this expression, like factoring the second term or solving for specific values of zz? Let me know if you need more details.

Here are a few related questions you might find interesting:

  1. How can we factor z3+1z^3 + 1 further?
  2. What happens when we set z9+z6=0z^9 + z^6 = 0 and solve for zz?
  3. What is the relationship between the factored form and the graph of this function?
  4. How do exponents work in polynomial expressions like this one?
  5. Can we apply this technique to higher degree polynomials?

Tip: When factoring expressions with multiple terms involving powers of a variable, always start by factoring out the smallest power of the variable. This simplifies the expression significantly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Factorization
Exponents

Formulas

Factorization: a^m + a^n = a^n(a^(m-n) + 1)

Theorems

Basic Factorization Theorem

Suitable Grade Level

Grades 9-12