https://file.aiquickdraw.com/mathbot/file/17263771396945czrwcgl.jpg

Let's solve each problem to find the greatest common factor (GCF) for the given expressions.

### Problem 4: 
Expression: \( 14x + 4xy - 18xy^2 \)

1. Factor out the common terms in each term:
   \[
   GCF = 2x
   \]
   Factoring:
   \[
   14x + 4xy - 18xy^2 = 2x(7 + 2y - 9y^2)
   \]
   
### Problem 5: 
Expression: \( 49mb^2 - 35m^2ba + 77ma^2 \)

1. Factor out the common terms in each term:
   \[
   GCF = 7m
   \]
   Factoring:
   \[
   49mb^2 - 35m^2ba + 77ma^2 = 7m(7b^2 - 5mba + 11a^2)
   \]

### Problem 6: 
Expression: \( 30x^2y - 45x^3y^2 + 135xy^3 \)

1. Factor out the common terms:
   \[
   GCF = 15xy
   \]
   Factoring:
   \[
   30x^2y - 45x^3y^2 + 135xy^3 = 15xy(2x - 3x^2y + 9y^2)
   \]

### Problem 7:
Expression: \( 200p^2m^3 - 30p^2m^3 + 40m^3 \)

1. Factor out the common terms:
   \[
   GCF = 10m^3
   \]
   Factoring:
   \[
   200p^2m^3 - 30p^2m^3 + 40m^3 = 10m^3(20p^2 - 3p^2 + 4)
   \]

### Problem 8:
Expression: \( 36j^4k^2 - 18j^5k^3 + 54j^4k^4 \)

1. Factor out the common terms:
   \[
   GCF = 18j^4k^2
   \]
   Factoring:
   \[
   36j^4k^2 - 18j^5k^3 + 54j^4k^4 = 18j^4k^2(2 - jk + 3k^2)
   \]

### Problem 9:
Expression: \( 6y^4 - 2y^3 + 3y^2 - y \)

1. Factor out the common terms:
   \[
   GCF = y
   \]
   Factoring:
   \[
   6y^4 - 2y^3 + 3y^2 - y = y(6y^3 - 2y^2 + 3y - 1)
   \]

---

Let me know if you'd like more details or explanations for any step!

Here are 5 related questions to explore further:

1. How do you determine the greatest common factor in a polynomial?
2. What are the differences between factoring polynomials and numbers?
3. Can you factor polynomials with more than two variables?
4. How does factoring relate to solving polynomial equations?
5. What happens if a polynomial has no common factors?

**Tip:** Always start by factoring out the greatest common factor (GCF) before attempting other methods of factorization!

Find the greatest common factor for the given polynomial expressions.

Learn how to find the greatest common factor (GCF) for polynomial expressions. This detailed guide covers multiple problems and teaches how to factor out common terms using algebraic techniques. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation