Factoring Algebraic Expressions Word Problems

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. Read the word problem and determine the greatest common factor of the 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

A rectangular garden is being separated into 6 equal sections for different types of flowers. The area of the garden is (12x + 30) square meters. What is the area of each section of the garden?

Solution

1. Find the greatest common factor of the two terms.
The greatest common factor of 12 and 30 is 6.

2. Keep the greatest common factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.
(12x + 30) = (6 ● 2x) + (6 ● 5)
6(2x + 5)

3. Verify your answer by multiplying the factors to get the original expression.
6(2x + 5)
12x + 30

Therefore, the area of each section of the garden is (2x + 5) square meters.

Practice Factoring Algebraic Expressions Word Problems

Practice Problem 1

Ralph spends 14z + 21 dollars every week. How much money does he spend daily?

Practice Problem 2

Each friend has ( $\fn_phv {\color{Teal} \frac{x}{4}}$ + 3) apples, and there are 4 friends. How many apples are there altogether?

Practice Problem 3

Sam shared his marbles with seven friends. Each friend has (7n – 1) marbles. How many marbles did Sam start with?

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