Factorisation is writing a polynomial as a product of several factors, usually simpler expressions of the same kind. In order to factorise a polynomial, we have to break it down to a smaller one or more than one product of various factors, which are then multiplied together to give the original number.
The students will learn to solve several algebraic expressions, such as monomials, binomials, trinomials, or polynomials. Factorisation formula containing quadratic polynomials is an important topic to discuss.
Otherwise, it cannot be factorised into non-constant real factors.
Factorisation formulas in algebra are very important when solving quadratic polynomials. While reducing the formulas, first of all, we have to remove all the brackets. For example, with fractional formulas, sometimes factorisation can be used to make the formula shorter. Some easily recognisable factorization patterns are
Sometimes, factorisation is not always possible, and when it is possible, the factors are not always simpler. Say an expression, x10 – 1 can be factored to two factors as
This chapter comprises several methods of factorisation. The methods discussed in the chapter include factorisation by using the common terms, factorisation by grouping the terms. The chapter also elaborates on factorisation using perfect squares, finding the factors by the difference of two squares, splitting the terms and taking out the sums and differences of two cubes.