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Factoring Polynomials Calculator
Factor polynomials step by step
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.
Solution
Your input: factor $$$4 x^{6} - 25$$$.
Apply the difference of squares formula $$$\alpha^{2} - \beta^{2} = \left(\alpha - \beta\right) \left(\alpha + \beta\right)$$$ with $$$\alpha = 2 x^{3}$$$ and $$$\beta = 5$$$:
$${\color{red}{\left(4 x^{6} - 25\right)}} = {\color{red}{\left(2 x^{3} - 5\right) \left(2 x^{3} + 5\right)}}$$
Thus, $$$4 x^{6} - 25=\left(2 x^{3} - 5\right) \left(2 x^{3} + 5\right)$$$.
Answer: $$$4 x^{6} - 25=\left(2 x^{3} - 5\right) \left(2 x^{3} + 5\right)$$$.