Factorization or factoring is the process that consists of writing a number or another number as a product of several factors, usually smaller or simpler objects of the same kind.
A factor is a number that divides that the given number.
Here we will express algebraic expressions as products of their factors or Factorization.
Like -: 5xy = 5 x X x Y.
When we factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions
The irreducible factor forms of 5xy and 10x are respectively, 5xy = 5 x x x y
10x = 2 x 5 x x
Regrouping may be possible in more than one ways. Suppose, we regroup the expression as: 2xy + 3x + 2y + 3. This will also lead to factors. Let us try:
2xy + 3x + 2y + 3
= 2 x x x y + 3 x x + 2 x y + 3
= x x (2y + 3) + 1 x (2y + 3)
= (2y + 3) (x + 1)
Factorisation using identities
(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
(a + b) (a − b) = a2 − b2
As we have learnt how to do add and subtract, multiplications with algebraic expressions.
Now we have to learn the division with algebraic expression here.
Like - :
6x3 ÷ 2x = 6x3/2x
= 2 x 3 x x x x x x/2 x x
= 3 x x x x
= 3x2
Consider (7x2 + 14x) ÷ (x + 2)
(7x2 + 14x) ÷ (x + 2) = 7x2 + 14x/x + 2
= 7x(x + 2)/x + 2
= 7x
Remember, when you multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).
Remember, when you square a monomial, the numerical coefficient and each factor has to be squared.
While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.