Question

How do you factor the expression \[{{x}^{2}}+2x-3\]\[?\]

Answer 1

Hint: To solve this question you must get the concept of factors and how to factorize the quadratic equation. The simple method used for this is splitting the middle term. Now to use this method firstly take a look at various steps used in this method. After knowing the steps you can solve this question.

Complete step-by-step answer:
The given expression for which we have to find the factor is \[{{x}^{2}}+2x-3\].
The general form of the quadratic equation is \[a{{x}^{2}}+bx+c\].
Where \[a,b\] and \[c\]are some constant value and there is a condition that \[a\ne 0\] because if \[a=0\]then the expression will no longer behave as the quadratic equation.
The easiest method to factor the quadratic expression is splitting the middle term method. Let us try to understand the concept of finding the factor of the quadratic expression by using the splitting the middle term method and then we will solve the given solution by the same method.
So for this procedure our first step is to find the two values such that product of that two values must be equal to the product of the coefficient of \[{{x}^{2}}\] i.e. \[a\]and the constant term i.e. \[c\] and the algebraic sum of that two numbers must be equal to the coefficient of \[x\] i.e. \[b\].
After that our next step is to split the middle term with the help of those two numbers. Now our next step is to take the common terms out from the first two and from the last two terms.
Now if the two numbers are chosen correctly then you are able to find the two factors of the quadratic equation. So these are the steps used to find the factor of the quadratic expression.
Now it is the time to solve the given expression \[{{x}^{2}}+2x-3\].
The two numbers which satisfies the condition are \[3\] and \[-1\]
So we can also write the given expression as
\[\Rightarrow {{x}^{2}}+3x-x-3\]
Now let us try to take the common terms out, we will get
\[\Rightarrow x(x+3)-1(x+3)\]
By simplifying the above expression we get
\[\Rightarrow (x-1)(x+3)\]
This means that \[(x-1)\] and \[(x+3)\] are the factors of the given expression \[{{x}^{2}}+2x-3\].
So, the correct answer is “\[(x-1)\] and \[(x+3)\]”.

Note: Factor of the expression is used to find the roots of the equation. Roots of any equation are very helpful to determine various kinds of information. It is also used to graph the equation. There is another method to get the roots of any equation and that method is by using Sridharacharya's formula.