Question

How do you solve the equation: $ {x^2} + 5x = 0? $

Answer 1

Hint: Factorization is the process of finding which prime numbers can be multiplied together to make the original number. Here we will first observe the given expression and then will find the common factors if any.

Complete step-by-step answer:
To find the factors of the algebraic expressions remember the identities relating to the sum and difference of cubes and sum and difference of squares formulas for an accurate and an efficient solution. Be good in square and cube numbers at least till twenty.
Take the given expression: $ {x^2} + 5x = 0 $
Find out the common multiple common outside the bracket.
 $ x(x + 5) = 0 $
Hence, the factors of $ {x^2} + 5x = 0 $ are $ x\;{\text{and }}(x + 5){\text{ }} $
This is the required solution.
So, the correct answer is “ $ x\;{\text{and }}(x + 5){\text{ }} $ ”.

Note: Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor.