- Representation of an algebraic expression as the product of two or more expressions is called factorisation.
- Each such expression is called a factor of the given algebraic expression.
- When we factorise an expression, we write it as a product of its factors.
- These factors may be numbers, algebraic (or literal) variables or algebraic expressions.
- A formula is an equation stating a relationship between two or more variables.
- For example, the number of square units in the area (A) of a rectangle is equal to the number of units of length (l) multiplied by the number of units of width (w).
- Therefore, the formula for the area of a rectangle is A = lw.
- Sometimes, you can evaluate a variable in a formula by using the given information.
- In the figure shown, the length is 9 units and the width is 5 units.
- A = lw
- A = 95
- A = 45
- The area is 45 square units or 45 units2.
- At other times, you must use your knowledge of equations to solve for a variable in a formula.
- An irreducible factor is a factor which cannot be expressed further as a product of factors. Such a factorisation is called an irreducible factorisation or complete factorisation.
- A factor which occurs in each term is called the common factor.
- The factorisation done by using the distributive law (property) is called the common factor method of factorisation.
- Sometimes, many of the expressions to be factorised are of the form or can be put in the form: a2 + 2ab + b2, a2 – 2ab + b2, a2 – b2 or x2 + (a + b) x + ab. These expressions can be easily factorised using identities: a2 + 2ab + b2 = (a + b) 2a2 – 2ab + b2 = (a – b) 2 a2 – b2 = (a + b) (a – b) x2 + (a + b) x + ab = (x + a) (x + b)
- In the division of a polynomial by a monomial, we carry out the division by dividing each term of the polynomial by the monomial.
- In the division of a polynomial by a polynomial, we factorise both the polynomials and cancel their common factors.

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