# 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, $$x^{2} + 4 x + 3 = 1 \left(x + 1\right) \left(x + 3\right)$$$. $$\color{red}{\left(x^{2} + 4 x + 3\right)} = \color{red}{1 \left(x + 1\right) \left(x + 3\right)}$$ Rewrite: $$1 \left(x + 1\right) \left(x + 3\right)=\left(x + 1\right) \left(x + 3\right)$$ Thus, $$x^{2} + 4 x + 3=\left(x + 1\right) \left(x + 3\right)$$$.

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