Explain Factorisation ?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
heya, buddy !!
=> When we break a number or a polynomial into a product of many factors of other polynomials, which when multiplied gives the original number, it is called factorisation.
For example - Prime Factorisation of 28 = 2 X 2 X 7 and
Product of 2 * 7 * 7 = 28 (Original Number).
We know that, there are only two types of numbers: Prime number and Composite number.
Before starting factorisation, let us first discuss an important mathematical term ‘Factor’.
know more , the Factors are the numbers, algebraic variables or an algebraic expression which divides the number or an algebraic expression without leaving any remainder.
For Example:
The factors of 42 = 2 × 3 × 7, the numbers 2, 3 and 7 are the factors of 42 and divide it without leaving any remainder.
The factors of an algebraic expression 10xyz = 2 × 5 × x × y × z.
Similarly,
The algebraic expression 5(x + 1) (z + 2) can be written in irreducible factor form as:
5(x + 1) (z + 2) = 5 × (x + 1) × (z + 2)
Now consider the algebraic expressions, 3y+12xy, 5x+10, x2 + x y + 8x and x2+2x+1, it is not so easy to tell their factors. To find factors of these expressions, we need to follow some methods of factorisation
Methods of Factorisation
Method of common factors
Step 1: Each term of given algebraic expression is written as a product of irreducible factors.
Step 2: The common factors are taken out and the rest of the expression is combined in the brackets.
For example 1: Factorise 6xy + 15yz
Step 1: we have, 6xy = 2 × 3 × x × y
15yz = 3 × 5 × y × z
Step 2: Common factors of these terms are 3 and y.
Therefore, 6xy + 15yz = (2 × 3 × x × y) + (3 × 5 × y × z)
6xy + 15yz = 3y (2x + 5z)
Explanation:
In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number. When you split a number into its factors or divisors, that's factorization. ... The word factorization comes from factor, which has had a mathematical meaning since the 1600s.