Factorisation is the process of breaking a number, an equation, or a polynomial into its basic components. This can be done by breaking the number into its prime factors, or by breaking the equation or polynomial into simpler forms. Factorisation is one of the most important topics in mathematics, as it is used in a variety of problems, from solving equations to finding the greatest common factor of numbers.
Why is Factorisation Important?
Factorisation is an important tool in mathematics because it can help simplify complex equations and problems. By breaking a complex problem into simpler forms, it is easier to manipulate the factors and solve the problem. Factorisation is used in a wide range of topics, including algebra, trigonometry, calculus, and number theory. It can also be used to simplify certain types of equations, such as quadratic equations, and to factorise polynomials.
How to Factorise an Equation
Factorising an equation is a process of breaking the equation into its simplest form. To do this, the equation must be rearranged so that all the terms are on one side, and the other side is equal to zero. Then the equation can be written in its factored form by dividing the terms by their common factors.
How to Factorise a Polynomial
Factorising a polynomial is a more complicated process than factorising an equation, as there may be multiple terms in the polynomial. To factorise a polynomial, the terms must be rearranged so that all the terms are on one side, and the other side is equal to zero. Then the polynomial can be written in its factored form by finding the greatest common factor of all the terms.
Factorise Each of the Following
When given a problem to factorise, the first step is to rearrange the equation or polynomial so that all the terms are on one side, and the other side is equal to zero. Then, the equation or polynomial can be written in its factored form by dividing the terms by their common factors.
Examples of Factorising
To demonstrate how to factorise an equation or polynomial, consider the following examples.
Equation: 5x + 10 = 0
Solution: 5x + 10 = 0
5x = -10
x = -2
Factored form: x = -2
Polynomial: x2 + 5x + 6
Solution: x2 + 5x + 6
x(x + 5) + 6
x(x + 5) = -6
x = -6/ (x + 5)
Factored form: x(x + 5) = -6
Conclusion
In conclusion, factorisation is an important tool in mathematics that can be used to simplify equations and polynomials into their simplest form. To factorise a problem, the equation or polynomial must be rearranged so that all the terms are on one side, and the other side is equal to zero. Then the equation or polynomial can be written in its factored form by dividing the terms by their common factors. Factorisation can be used in a variety of topics, such as algebra, trigonometry, calculus, and number theory.
