Question

How do you write \[{x^2} + 4x + 3\] in factored form?

Answer 1

Hint: Here, we will use the concept of the factorization. First, we will split the middle term of the equation. Then we will form the factors by taking the common terms in the equation to get the equation in the factored form.

Complete step by step solution:
Given equation is \[{x^2} + 4x + 3\].
Factorization is the process in which a number is written in the form of its small factors which on multiplication give the original number.
First, we will split the middle term into two parts such that its multiplication will be equal to the product of the first term and the third term of the equation. Therefore, we get
\[ \Rightarrow {x^2} + 4x + 3 = {x^2} + 3x + x + 3\]
Now we will be taking \[x\] common from the first two terms and taking 1 common from the last two terms. Therefore the equation becomes
\[ \Rightarrow {x^2} + 4x + 3 = x\left( {x + 3} \right) + 1\left( {x + 3} \right)\]
Now we will take \[\left( {x + 3} \right)\] common from the equation. So, we get
\[ \Rightarrow {x^2} + 4x + 3 = \left( {x + 3} \right)\left( {x + 1} \right)\]

Hence the factored form of the equation \[{x^2} + 4x + 3\] is equal to \[\left( {x + 3} \right)\left( {x + 1} \right)\].

Note:
A quadratic equation is an equation that has the highest degree of 2 and has two solutions. Here we should split the middle term according to the basic condition. The condition is that a term with the single power of the variable should be divided in such a way that its product must be equal to the product of the first and the last term of the equation. Factors are the smallest part of the number or equation which on multiplication will give us the actual number of equations.