FACTORIZATION

Factorization

Definition Of Factorization

Factorization is a method of writing numbers as the product of their factors or divisors.

More About Factorization

When the factors of a number are multiplied together, they give the original number.
Normally factorization is done by using prime factorization method.

Video Examples:How to Factor any Quadratic Equation

Example of Factorization

By using the method of factorization(prime factorization), 21 can be written as 21 = 3 × 7.
25p³ + 10p² can be factorized as 5p²(p + 2).

Solved Example on Factorization

Ques: Factor:
24x² - 144x + 216

Choices:

A. 24(x - 3) (x + 3)
B. 24(x + 3)
C. 25(x - 3)²
D. 24(x - 3)²
Correct Answer: D

Solution:

Step 1: 24x² - 144x + 216 [Original expression.]
Step 2: = 24[x² - 6x + 9] [Take out common factor.]
Step 3: = 24[(x)² - 2(x)(3) + (3)2] [Write as (a² - 2ab + b²).]
Step 4: = 24[(x - 3)²] [Write as (a - b)².]

Quick Summary

Factorization expresses a number as a product of its factors.
Prime factorization is a common method.
When factors are multiplied, they yield the original number.

\[ N = f_1 \times f_2 \times ... \times f_n \]

🍎 Teacher Insights

Emphasize the difference between factors and multiples. Use visual aids like factor trees. Start with simple numbers and gradually increase complexity.

🎓 Prerequisites

Multiplication
Division
Prime Numbers

Check Your Knowledge

Q1: What are the factors of 21?

A. 1, 3, 7 B. 3, 7, 21 C. 1, 3, 7, 21 D. 1, 21

Q2: Factor 24x^2 - 144x + 216

A. 24(x - 3) (x + 3) B. 24(x + 3) C. 25(x - 3)^2 D. 24(x - 3)^2

Frequently Asked Questions

Q: What is prime factorization?
A: Prime factorization is expressing a number as a product of its prime factors.

Q: How is factorization used?
A: Factorization is used to simplify expressions, solve equations, and in cryptography.