How to Factor Polynomials by Taking a Common Factor?
A factor is a number that divides the given number without any remainder. It simply means expressing a number as a product of two other numbers. In this guide, you will learn more about factoring polynomials by taking a common factor.

The process of finding two or more expressions whose product is the given expression is known as the factorization of expressions.
Related Topics
A step-by-step guide to factoring polynomials by taking a common factor
The factor is a term used to express a number as a product of both numbers. Factorization is a way to find the factors of any mathematical object, whether it is a number, a polynomial, or an algebraic expression. Therefore, factorization of an algebraic expression refers to finding the factors of a given algebraic expression.
Follow the steps given below to find the factors of the expression by taking a common factor: \(x^2+4x\)
- Step 1: \(x^2\) can be factorized as \(x×x\), and \(4x\) can be factorized as \(x×4\).
- Step 2: Find the greatest common factor of these two terms. Here, we see that \(x\) is the largest common factor. Keep this coefficient out of parentheses, divide the polynomial expressions by this coefficient, and write the remaining expression inside the brackets.
- Step 3: Thus, the expression is factorized as \(x(x+4)\).
Factoring Polynomials by Taking a Common Factor – Example 1:
Factorize \(5z^3−15z^2\).
Solution:
The first term \(5z^3\) can be factorized as \(5×z×z×z\) and the second term \(15z^2\) can be factorized as \(15×z×z\).
The common factor for both terms is \(5z^2\).
Taking out the common factor, we get the factors \(5z^2(z−3)\).
Therefore, the factors of \(5z^3−15z^2\) are \(5z^2(z−3)\).
Exercises for Factoring Polynomials by Taking a Common Factor
Factorize the following expression by taking a common factor.
- \(\color{blue}{7x^2y+21xy^2}\)
- \(\color{blue}{6x^2y+14xy^2-42xy-2x^2y^2}\)
- \(\color{blue}{9x^5y^3+24x^3y^2-18x^2y}\)
- \(\color{blue}{32x^3y^3+56x^4y-40x^3y}\)
- \(\color{blue}{120x^3yz^3+32x^4y^2-68x^2y^2z}\)

- \(\color{blue}{7xy\left(x+3y\right)}\)
- \(\color{blue}{2xy\left(y-3\right)\left(-x+7\right)}\)
- \(\color{blue}{3x^2y\left(3x^3y^2+8xy-6\right)}\)
- \(\color{blue}{8x^3y\left(4y^2+7x-5\right)}\)
- \(\color{blue}{4x^2y\left(30xz^3+8x^2y-17yz\right)}\)
More math articles
- Intelligent Math Puzzle – Challenge 89
- Easy Ways To Overcome Your Fear Of Math
- ISEE Upper-Level Math Worksheets: FREE & Printable
- TExES Core Subjects Math- Test Day Tips
- FREE 7th Grade ACT Aspire Math Practice Test
- What is the Best Laptop for College Students?
- TSI Math FREE Sample Practice Questions
- Trigonometric Ratios
- FREE 8th Grade Georgia Milestones Assessment System Math Practice Test
- The Best Calculator for FE Exam
What people say about "How to Factor Polynomials by Taking a Common Factor?"?
No one replied yet.