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100 LearnersLast updated on September 25, 2025
Math Formula for Factorization
In mathematics, factorization involves breaking down a number or an expression into a product of its factors. These factors can be numbers, variables, or algebraic expressions. In this topic, we will learn the formulas for factorization.
List of Math Formulas for Factorization
Factorization is a crucial concept in algebra and arithmetic. Let’s learn the formulas and methods to factorize numbers and expressions.
Math Formula for Factorizing Numbers
Factorizing numbers involves expressing a number as a product of its prime factors.
For example, the factorization formula for 60 is 60 = 2 × 2 × 3 × 5.
Math Formula for Factorizing Quadratic Expressions
Factorizing quadratic expressions often involves the quadratic formula or methods like completing the square.
For example, the quadratic expression x² + 5x + 6 can be factored as (x + 2)(x + 3).
Math Formula for Factorizing Cubic Expressions
Factorizing cubic expressions can involve grouping or the use of formulas such as:
For example, the expression x³ - 6x² + 11x - 6 can be factored as (x - 1)(x - 2)(x - 3).
Importance of Factorization Formulas
In mathematics and real-world applications, factorization formulas are used to simplify expressions and solve equations.
Here are some important uses of factorization:
- Factorization helps simplify complex algebraic expressions.
- It is crucial for solving polynomial equations.
- Factorization aids in finding roots of equations and simplifying fractions.
Tips and Tricks to Memorize Factorization Math Formulas
Students often find factorization challenging.
Here are some tips and tricks to master factorization formulas:
- Practice by solving numerous examples to recognize patterns.
- Use mnemonic devices to remember specific formulas, such as “SOAP” for factoring the sum and difference of cubes.
- Draw diagrams or create analogies to better understand the factorization process.
Common Mistakes and How to Avoid Them While Using Factorization Math Formulas
Students make errors when applying factorization formulas. Here are some mistakes and the ways to avoid them, to master them.
Mistake 1
Ignoring Prime Factorization
Students sometimes overlook the prime factorization process for numbers, leading to incomplete results.
To avoid this, ensure that all factors are prime and correctly multiplied.
Mistake 2
Misapplying the Quadratic Formula
When factorizing quadratics, students may misapply the quadratic formula.
To avoid this, carefully check each step of the calculation and verify the solution by expanding the factors.
Mistake 3
Confusing Sum and Difference of Cubes
Students often confuse the formulas for the sum and difference of cubes.
To avoid this, memorize the specific formulas: a³ + b³ = (a + b)(a² - ab + b²) a³ - b³ = (a - b)(a² + ab + b²)
Mistake 4
Skipping the Factoring Step
Students might skip initial factoring steps, leading to more complex equations.
To avoid this, always start by factoring out any common terms before applying other factorization methods.
Mistake 5
Incorrect Application of Grouping
When factorizing by grouping, students sometimes make errors in grouping terms.
To avoid this, ensure that the grouped terms have a common factor and check the factorization by expanding.
Examples of Problems Using Factorization Math Formulas
Problem 1
Factorize 120 into its prime factors.
The prime factorization of 120 is 2 × 2 × 2 × 3 × 5.
Explanation
To find the prime factors of 120, start by dividing by the smallest prime number:
120 ÷ 2 = 60 60 ÷ 2 = 30 30 ÷ 2 = 15 15 ÷ 3 = 5 5 is a prime number.
Therefore, the prime factorization is 2 × 2 × 2 × 3 × 5.
Problem 2
Factorize the quadratic expression x² + 7x + 10.
The factorization is (x + 2)(x + 5).
Explanation
To factorize x² + 7x + 10, find two numbers that multiply to 10 and add to 7:
These numbers are 2 and 5.
Thus, x² + 7x + 10 = (x + 2)(x + 5).
Problem 3
Factorize x³ - 9x² + 27x - 27.
The factorization is (x - 3)³.
Explanation
To factorize x³ - 9x² + 27x - 27, notice the expression is a perfect cube:
x³ - 9x² + 27x - 27 = (x - 3)³.
Problem 4
Factorize 36 into its prime factors.
The prime factorization of 36 is 2 × 2 × 3 × 3.
Explanation
To find the prime factors of 36, start by dividing by the smallest prime number:
36 ÷ 2 = 18 18 ÷ 2 = 9 9 ÷ 3 = 3 3 is a prime number.
Therefore, the prime factorization is 2 × 2 × 3 × 3.
Problem 5
Factorize the expression x² - 4x + 4.
The factorization is (x - 2)².
Explanation
To factorize x² - 4x + 4, notice that it is a perfect square trinomial:
x² - 4x + 4 = (x - 2)².
FAQs on Factorization Math Formulas
1.What is the prime factorization of a number?
2.How to factorize a quadratic expression?
3.What is the formula for factoring the sum of cubes?
4.What is the factorization of x² + 8x + 16?
5.How do you factor a cubic expression?
Glossary for Factorization Math Formulas
- Factorization: The process of breaking down a number or expression into a product of factors.
- Prime Factorization: The expression of a number as a product of its prime factors.
- Quadratic Expression: A polynomial expression of degree two.
- Cubic Expression: A polynomial expression of degree three.
- Perfect Square Trinomial: A quadratic expression that is the square of a binomial.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
