Question

What is the factorization of \[4{x^2} + 6x = 0\]?

Answer 1

Hint: For solving this equation first of all we should be aware of factorization, its method and its properties. The process of writing a number as a product of several factors. When factors are multiplied together then they form the original number as in the beginning.

Complete step by step answer:
The most common method of factorization is to completely factor the number into its positive prime factors. The number which has only positive factor one and the number itself, is termed as the prime number. Factoring is just the reverse of expanding brackets.
The factors of any given equation may be an integer, an algebraic expression or a variable or itself.
For example 6 and 3 are the factors of 18. There are six methods to solve factorization. These are Greatest Common Factor, Grouping Method, Sum or difference in two cubes, Difference in two squares method, General trinomials and Trinomial method.

Now we will solve the following equation by the use of factorization method. \[4{x^2} + 6x = 0\] ----------(i) eq

We can also write the equation (i) as $2x({2x + 3})= 0$ -------(ii)eq
Now putting the eq(ii) equal to zero, we will get the value of x.
Hence, for $2x = 0 $ then $x = 0$
And for $2x + 3 = 0$ then $x = - \dfrac{3}{2}$

Thus, the factors of \[4{x^2} + 6x = 0\] are $0$ and $- \dfrac{3}{2}$

Note: Factorization is an important process, which helps us understand more about the equations. Through factorization, usually we rewrite the polynomials in its simpler form, and when we use factorization’s principles in any equation, we find a lot of useful information about it. The ancient Greek Mathematicians were the first one who considered the factorization in the case of integers.