Question

What are the methods of factorisation?

Answer 1

Answer:

Factoring out the GCF.

The sum-product pattern.

The grouping method.

The perfect square trinomial pattern.

The difference of squares pattern.

Answer 2

Answer:

Types of Factoring polynomials

There are six different methods to factorise the polynomials. The six methods are as follows:

Greatest Common Factor (GCF)

Grouping Method

Sum or difference in two cubes

Difference in two squares method

General trinomials

Trinomial method

In this article, let us discuss the two basic methods which we are using frequently to factorise the polynomial. Those two methods are the greatest common factor method and the grouping method. Apart from these methods, we can factorise the polynomials by the use of general algebraic identities. Similarly, if the polynomial is of a quadratic expression, we can use the quadratic equation to find the roots/factor of a given expression. The formula to find the factor of the quadratic expression (ax2+bx+c) is given by:

x=−b±b2−4ac√2a

Greatest Common Factor

We have to find out the greatest common factor, of the given polynomial to factorise it. This process is nothing but a type of reverse procedure of distributive law, such as;

p( q + r) = pq + pr

But in the case of factorisation, it is just an inverse process;

pq + pr = p(q + r)

where p is the greatest common factor.

Factoring Polynomials By Grouping

This method is also said to be factoring by pairs. Here, the given polynomial is distributed in pairs or grouped in pairs to find the zeros. Let us take an example.

Example: Factorise x2-15x+50

Find the two numbers which when added gives -15 and when multiplied gives 50.

So, -5 and -10 are the two numbers, such that;

(-5) + (-10) = -15

(-5) x (-10) = 50

Hence, we can write the given polynomial as;

x2-5x-10x+50

x(x-5)-10(x-5)

Taking x – 5 as common factor we get;

(x-5)(x-10)

Hence, is the answer.

Factoring Using Identities

The factorisation can be done also by using algebraic identities. The most common identities used in terms of the factorisation are:

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

a2 – b2= (a + b)(a – b)

Let us see an example:

Factorise (x2 – 112)

Using the identity, we can write the above polynomial as;

(x+11) (x-11)

Factor theorem

For a polynomial p(x) of degree greater than or equal to one,

x-a is a factor of p(x), if p(a) = 0

If p(a) = 0, then x-a is a factor of p(x)

Where ‘a’ is a real number.

Step-by-step explanation:

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