Question

What are the factors of \[{{x}^{2}}+y-xy-x\] ?

Answer 1

Hint: To solve this type of problem, first understand the concept of quadratic equation, after that observe the given quadratic equation and then try to find out the factors of the equation by taking common and then you will get your required answer.

Complete step-by-step solution:
The word 'Quadratic Equations’ is derived frоm the соmbinаtiоn оf ‘quad’, whiсh means squаre аnd ‘equation’. Hence, the Quаdrаtiс equation аlwаys hаs а second degree where the exроnent is squаre аnd аlwаys equal to zero. In other words, we can also say that the polynomial equation in which the highest degree is two can be called the quadratic equation.
There are many different ways or methods to solve the quadratic equation such as: Factoring, Completing the square, Using Quadratic formula and taking the square root.
As when we want to solve the quadratic equation using factoring, then first we need to ensure that the equation is in the quadratic form (i.e. it should be a second degree equation). After that it is necessary to ensure that the given equation is set to adequate zero, after that try to factor the left side of the equation by taking something common or by adding or subtracting, assuming that there is zero on the right hand side of the equation. After you get all the factors, assign each factor equal to zero and then try to find out the value of the variable. In this way you will solve any given quadratic equation through a factoring method.
We also use the Sridharacharya method to solve the quadratic equations. Sridhara wrote down rules for solving quadratic equations, it is the most common method of finding the roots of the quadratic equation and it is known as Sridharacharya rule.
 Now, according to the given question:
Given quadratic equation:
\[{{x}^{2}}+y-xy-x\]
\[\Rightarrow {{x}^{2}}-xy+y-x\]
To get the factors of the quadratic equation, we are taking common:
\[\Rightarrow x(x-y)-1(x-y)\]
\[\Rightarrow (x-1)(x-y)\]
So, the factors of \[{{x}^{2}}+y-xy-x\] are \[(x-1)(x-y)\].

Note: Quadratic equations are used in many real life word problems, such as speed problems, time problems, distance problems and geometry area problems etc. Also used in solving problems like finding areas of any quadrilateral such as rectangle, parallelogram, rhombus etc.