# Factorization Challenge

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## 10 Questions

### What is the factorization of the integer 15?

$3 imes 5$

### What is the factorization of the polynomial $x^2 - 4$?

$(x - 2)(x + 2)$

### What does factorization consist of?

Writing a number as a product of factors

### Is factorization considered meaningful within number systems possessing division?

No, except for rational numbers or functions

### Who first considered factorization?

Ancient Greek mathematicians

### What is a meaningful factorization for a rational number or a rational function?

Writing it in lowest terms and separately factoring its numerator and denominator

### What can any non-zero $x$ be trivially written as, within number systems possessing division?

$(xy) imes (1/y)$

### What does the fundamental theorem of arithmetic assert?

Every integer can be factored into prime numbers

### Why is factorization not usually considered meaningful within number systems possessing division?

Because any $x$ can be trivially written as $(xy) imes (1/y)$ whenever $y$ is not zero

### What is a factorization of a mathematical object?

Writing it as a product of several factors

Test your knowledge of factorization with this quiz! Explore the concept of writing numbers and mathematical objects as a product of factors. Challenge yourself with various examples and strengthen your understanding of factorization.

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