Question

What are the different methods to factorise a equation?answer by giving example.

Answer 1

1. Factorisation with a common monomial
♦Step 1: Find the common factor, which will be the greatest monomial that can divide each term in the polynomial. This common factor will be the HCF of all terms of the polynomial.
♦ Step 2: Divide each term of the polynomial by the common factor found in Step 1.
♦ Step 3: Write the common factor before a pair of brackets enclosing all the quotients obtained in Step 2.

2. Grouping method
All the terms of a polynomial may not have a common factor, but upon closer inspection we may find that some terms have a common factor to them. The grouping method involves bringing together such terms that have a common factor.

3. Factorising the difference of two squares
If an algebraic expression is the difference of two squares, it can be factorised by this method.
♦ Step 1: The common factor, if any is taken out and all terms of the expression are divided by it.
♦ Step 2: The square root of each term is calculated.
♦Step 3: The sum of the square roots is one factor and the difference of the square roots is the other factor.