Factor: 15xy3 + 10x2y.
5(3xy2 + 2x2y)
5xy(3y2 + 2x)
5xy(3y - 2x)
5x(3y2 + 2x)


To factor the expression \( 15xy^3 + 10x^2y \), let's go step by step:

1. **Factor out the greatest common factor (GCF)** from both terms. The GCF of \( 15xy^3 \) and \( 10x^2y \) is \( 5xy \).

2. **Divide both terms by the GCF**:
   \[
   \frac{15xy^3}{5xy} = 3y^2
   \]
   \[
   \frac{10x^2y}{5xy} = 2x
   \]

So, factoring out \( 5xy \), we get:
\[
5xy(3y^2 + 2x)
\]

Thus, the correct factorization is:
\[
\boxed{5xy(3y^2 + 2x)}
\]

Let me know if you need further explanation or if you'd like more details!

Here are 5 related questions to deepen your understanding:
1. How do you find the greatest common factor in a polynomial?
2. What happens if there is no common factor between terms in a polynomial?
3. How would you factor an expression like \( 20x^3y + 15x^2y^2 \)?
4. How can factoring help simplify polynomial expressions?
5. Can a factor be a binomial or a higher-degree polynomial?

**Tip:** Always look for the GCF first before attempting other factoring techniques, as it simplifies the problem!

Factor: 15xy^3 + 10x^2y. 5(3xy^2 + 2x^2y) 5xy(3y^2 + 2x) 5xy(3y - 2x) 5x(3y^2 + 2x)

Learn how to factor the polynomial expression 15xy^3 + 10x^2y using the greatest common factor method. This step-by-step solution demonstrates factoring out the GCF, simplifying the expression, and applying key algebraic concepts. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation