Factoring by grouping calculator works on the principle by splitting the middle term in the quadratic equation into two terms, so that their product is equal to the constant term and their sum is equal to the second term in the polynomial.

That is $x^{2} + 4x + 3$ = $x^{2} + 3x + x + 3$

where, $3x + x$ = $4x$ (the middle term)

$3 \times 1 = 3$ (the constant term)

Group the equation by taking out the common terms.

That is, $x^{2} + 3x + x + 3$ can be written as $x(x + 3) +1(x + 3)$

= $(x + 3) (x + 1)$

Here $x = -3$ and $x = -1$ are the factors of given equation.