# Factoring Polynomials Calculator

The calculator will try to factor any polynomial (binomial, trinomial, quadratic, etc.), with steps shown. The following methods are used: factoring monomials (common factor), factoring quadratics, grouping and regrouping, square of sum/difference, cube of sum/difference, difference of squares, sum/difference of cubes, the rational zeros theorem. The calculator accepts both univariate and multivariate polynomials.

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## Solution

Your input: factor $x^{2} + 4 x + 3$.

To factor the quadratic function $x^{2} + 4 x + 3$, we should solve the corresponding quadratic equation $x^{2} + 4 x + 3=0$.

Indeed, if $x_1$ and $x_2$ are the roots of the quadratic equation $ax^2+bx+c=0$, then $ax^2+bx+c=a(x-x_1)(x-x_2)$.

Solve the quadratic equation $x^{2} + 4 x + 3=0$.

The roots are $x_{1} = -1$, $x_{2} = -3$ (use the quadratic equation calculator to see the steps).

Therefore, $x^{2} + 4 x + 3 = \left(x + 1\right) \left(x + 3\right)$.

$$\color{red}{\left(x^{2} + 4 x + 3\right)} = \color{red}{\left(x + 1\right) \left(x + 3\right)}$$

Thus, $x^{2} + 4 x + 3=\left(x + 1\right) \left(x + 3\right)$.

Answer: $x^{2} + 4 x + 3=\left(x + 1\right) \left(x + 3\right)$.