Question

How do you factor $ 2{{x}^{2}}-4x $ ?

Answer 1

Hint: In this question, we have to find the greatest common factor of the given polynomial to factorize it. For example, we are given: pq + pr. So, the greatest common factor will be p as p(q + r). To find the greatest common factor is just like the reverse of the distributive law.

Complete step by step answer:
The reverse procedure of multiplication of factors of polynomials is called the factorization of the polynomials. We use to find the greatest common factor of the given polynomial to factorize it. And after factorization of a given polynomial, if we divide the polynomial with any of its factors, the remainder will come out to be zero.
There are various methods in which we can factorize the given polynomial. The most common methods are Greatest Common Factor (GCF), the grouping method, sum or difference in two cubes, the difference in two square method, general trinomials, and trinomial method.
We have algebraic identities too apart from these methods to factorize the polynomials.
Let’s discuss some of the methods now.
The first method is the Greatest Common Factor (GCF). We have to find the GCF of the given polynomial to factorise it. It is basically the reverse of the distributive law.
The second method is the grouping method. Factoring is done in the form of pairs.
Now, let’s solve the given question using the GCF method of the polynomials.
 $ \Rightarrow 2{{x}^{2}}-4x $
Now take 2x common from both the terms. We get:
 $ \Rightarrow 2x(x-2) $
So the factors are: 2x and (x – 2).

Note:
You should be aware of all the methods of factorization so that whenever you get any question about factorization, you can easily solve it. There is no need to find the zeroes. There is a possibility that students might take out x as common or 2 as common and not both. They must note that every factor that is common to both terms must be taken out as common. So, this must be taken care of.