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