# 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.

## 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 forFactoring Polynomials by Taking a Common Factor

### Factorize the following expression by taking a common factor.

1. $$\color{blue}{7x^2y+21xy^2}$$
2. $$\color{blue}{6x^2y+14xy^2-42xy-2x^2y^2}$$
3. $$\color{blue}{9x^5y^3+24x^3y^2-18x^2y}$$
4. $$\color{blue}{32x^3y^3+56x^4y-40x^3y}$$
5. $$\color{blue}{120x^3yz^3+32x^4y^2-68x^2y^2z}$$
1. $$\color{blue}{7xy\left(x+3y\right)}$$
2. $$\color{blue}{2xy\left(y-3\right)\left(-x+7\right)}$$
3. $$\color{blue}{3x^2y\left(3x^3y^2+8xy-6\right)}$$
4. $$\color{blue}{8x^3y\left(4y^2+7x-5\right)}$$
5. $$\color{blue}{4x^2y\left(30xz^3+8x^2y-17yz\right)}$$

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