Factorize ${x^2} + 4x + 3$

Hint: Factorization: factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
To solve this question we should first try to split the middle term which is given with respect to the product of coefficients of first and last term. Then we will take a common and try to reduce it further.

Complete answer:As given,
${x^2} + 4x + 3$
We have to factorize it.
Show we will take coefficient and first and last constant term.
Here, $a = 1\,and\,c = 3$
And $b = 4$
Product of $a\,and\,b = 3 \times 1 = 3$
So, we will split 4 will in respect to 3.
So, we can write $4 = 3 + 1$
Let keeping it in equation:
${x^2} + 4x + 3$
Keep as above calculated:
${x^2} + (3 + 1)x + 3$
Open the bracket,
${x^2} + x + 3x + 3$
Take common from first two and last two terms.
$x(x + 1) + 3(x + 1)$
Take the common from it. We get,
 $ = (x + 1)\left( {x + 3} \right)$
So, on doing the Factorization,we have ${x^2} + 4x + 3 = (x + 1)\left( {x + 3} \right)$

Note:
If you want to calculate zeros of a given quadratic equation. Then we will keep it equal to zero.
As,
 $(x + 1)\left( {x + 3} \right) = 0$
So, $(x + 1) = 0$
$ \Rightarrow x = - 1$
And $\left( {x + 3} \right) = 0$
$ \Rightarrow x = - 3$
Zero: It is the value at which our given equation will be zero.