**Factorisation in Z-H**
In mathematics, factorisation is the process of expressing a given number or algebraic expression as a product of other numbers or expressions, known as factors. In this article, we will explore the concept of factorisation in the Z-H language. Z-H, short for Zhong Hua, is a programming language developed in China that is widely used in various domains, including education and finance.
**Why Factorisation?**
Factorisation has several benefits and applications in mathematics and programming, including:
* Simplification of expressions
* Finding common factors
* Solving equations
* Optimising code
**Types of Factorisation**
There are two main types of factorisation:
1. **Integer Factorisation**: Decomposing an integer into smaller integers
2. **Polynomial Factorisation**: Decomposing a polynomial into smaller polynomials
**Factorisation Methods in Z-H**
Z-H provides several built-in functions and operators for factorisation, making the process straightforward. Let’s explore the most commonly used methods:
* **Direct Factorisation**: Using the `factor` function, you can directly factorise an integer or a polynomial. For example:
“`Z-H
zh> A = 12
zh> factor(A)
[2, 2, 3]
“`
* **Prime Factorisation**: To obtain the prime factors of an integer, you can use the `primeFactors` function. For instance:
“`Z-H
zh> B = 24
zh> primeFactors(B)
[2, 2, 2, 3]
“`
* **Polynomial Factorisation**: For factorising polynomials, Z-H offers the `factorPoly` function. Let’s try an example:
“`Z-H
zh> C = x^2 + 2x – 3
zh> factorPoly(C)
[(x + 3), (x – 1)]
“`
**Case Study: Solving a Quadratic Equation**
Let’s consider a quadratic equation: `ax^2 + bx + c = 0`. Using factorisation, we can solve for the roots of the equation. Here’s how it works in Z-H:
1. Factorise the quadratic polynomial `ax^2 + bx + c` using `factorPoly`. This will give you two linear factors, `(px + q)` and `(rx + s)`..
2. Set each factor to zero and solve for `x`:.
“`Z-H.
zh> px + q = 0.
zh> rx + s = 0.
“`.
3. The solutions to these equations will give you the roots of the quadratic equation..
**Conclusion**
Factorisation is a fundamental concept in mathematics and programming. Z-H provides powerful functions and operators that simplify factorisation tasks. By understanding the different factorisation methods available in Z-H, you can effectively work with integers and polynomials, solve equations, and optimise your code. Whether you are a student, a researcher, or a software developer, leveraging factorisation techniques in Z-H can enhance your problem-solving abilities and streamline your programming endeavors..
