Factorisation definition

In Mathematics, factorization (factorization in British English) or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

It is simply the resolution of an integer or polynomial into factors such that when multiplied together they will result into original or initial the integer or polynomial.

Math factoring

To factor, a number means to break it up into numbers that can be multiplied to get the original number. For example, 24 = 6 x 4 so, factors of 24 are 6 and 4, 9 = 3 x 3. Therefore, factors of 9 are 3 and 3. Also, numbers can be factorized into different combinations.

Factoring in algebra

The numbers -12, -6, -2, -1, 1, 2, 6, and 12 are all factors of 12 because they divide 12 without a remainder. It is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations. It is also called as Algebra factorization.

Maths factorization formula for a quadratic equation:

A “quadratic” is a polynomial that is written like “ax^{2} + bx + c”, where “a”, “b”, and “c” are just numbers. For an easy case of factoring, you can identify the two numbers that will not only multiply to equal the constant term “c” but also add up to equal “b,” the coefficient on the x-term.

Factorising formulas are especially important when solving quadratic equations. When reducing formulas we normally have to remove all the brackets, but in particular cases, for example with fractional formulas, sometimes we can use factorisation to shorten a formula.

Terms and Factors

What is a Term?

It is something which is to be added or subtracted (subtracting is adding a negative number).

What is a Factor?

It is something that is to be multiplied.

Sum = term + term

Product = factor × factor

For example :

p = 4(2q – 6)

The 4 and 2q – 6 in the above formula are factors which are multiplied.

In factors 2q – 6 are 2q and –6 terms which are added.

In the term 2q have the 2 and q as factors.

Factorisation in Maths

Here are some factorization Math examples:

Factorise the quadratic equation:

x^{2} + 7x + 6

The constant term is 6, which can be written as the product of 2 and 3 or of 1 and 6. But 2 + 3 = 5, so 2 and 3 are not the numbers I need in this case. On the other hand, 1 + 6 = 7, so you can use 1 and 6:

x^{2} + 7x + 6 = (x+1)(x+6)

Note that the order doesn’t matter in multiplication, so the above answer can be written as “(x + 6)(x + 1).”

Solve the model solutions to the chapter Factorisation that are provided in detail through simple step-step solutions to all questions in an NCERT textbooks only at BYJU’S.