Factorising Polynominals

Factorising Polynomials

Understanding Factorising Polynomials

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Factorising is the process of breaking down the polynomial into its simplest factors.
These simple factors, when multiplied together, will yield the original polynomial.

Basics of Factorising Polynomials

Any equation that can be rewritten as the product of simpler polynomials can be considered as factorised.
Simple factors include polynomials of degree one and binomial terms with degree two; these are key targets when factorising.
The Coefficient (number before x) and Constant (number on its own) play a crucial role in factorising.

Factorising Methods

The simplest form of factorising includes taking out the common factor among the terms of the polynomial.
Grouping is another method of factorisation used when a polynomial has four or more terms.
Factoring by difference of squares is a method used when a polynomial is in the form of a² - b². This can be factorised to (a - b)(a + b).
Polynomials of third degree or higher can be factored by synthetic division or long division, which require more advanced methods for factorisation.

Factor Theorem

The Factor Theorem states that if f(a) = 0 for a polynomial f(x), then (x - a) is a factor of f(x).
By setting the polynomial equal to 0 and solving, candidates can find potential factors.
Substituting any value of a from the solution into the equation, if it equates to 0, confirms that the solution is indeed a factor according to the Factor Theorem.

Importance of Factorising in Algebraic Skills

Factorising is an essential algebraic skill as it simplifies complex equations and makes them easier to solve.
It also provides important insights into the equation, such as its roots and factors; knowing these can lead to quicker solutions for complex problems.
Understanding how to factorise efficiently and accurately is therefore key to overall algebraic competency.

Learn about factorising polynomials and strive for proficiency in its methods. This skill will assist in solving substantially more complex mathematical problems in a straightforward manner. Arrowed boxes preceding each bullet point emphasise points of importance or useful tips to be aware of.