Factor Algebraic Expressions

Concept

Factorization of algebraic means finding the factors of the given expression which refers to finding two or more expressions whose product is the given expression. This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions. A factor is a number that divides the given number without any remainder. It simply means expressing a number as a multiplication of two other numbers. Similarly, in Algebra we write the algebraic expressions as a product of their factors. The only difference here is that an algebraic expression involves numbers and variables combined with an arithmetic operation like addition or subtraction.

Rules

1. Find the greatest common factor of the two terms.
2. Keep the greatest common factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.
3. Verify your answer by multiplying the factors to get the original expression.

Example

Factorize the expression.
-45x – 5

Solution

1. Find the greatest common factor of the two terms.
The greatest common factor of -45 and -5 is -5.

2. Keep the greatest common factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.
-45x – 5 = (-5 ● 9x) + (-5 ● 1)
-5(9x + 1)

3. Verify your answer by multiplying the factors to get the original expression.
-5(9x + 1)
-45x – 5

Therefore, -45x – 5 = -5(9x + 1)

Practice Factor Algebraic Expressions

Practice Problem 1

Factor the expression.
16 + 18n

Practice Problem 2

Factor the expression.
$\fn_phv \frac{2}{5}x+7$

Practice Problem 3

Factor the expression.
-17xy – 34xyz

Factor – is a number that divides the given number without any remainder.

Linear Expression – an algebraic expression in which the variable is raised to the first power, and variables are not multiplied or divided.

Term – either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.

Like terms – Terms that have the same power for the same variables. In like terms, one can only change the numerical coefficient.

Unlike terms – Terms that have different variables or the same variables raised to different powers.

Distributive Property – to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.

Constant – a term without a variable.

Variable – In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation or expression.

Coefficient – is an integer that is multiplied with the variable of a single term or the terms of a polynomial.

Pre-requisite Skills
Identify Factors
Greatest Common Factor-GCF
Arithmetic Sequences
Geometric Sequences
The Distributive Property
Simplifying Complex Algebraic Expressions
Add Linear Expressions
Subtract Linear Expressions