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How to factor 3rd degree polynomials

!To solve a 3rd-degree polynomial, we have to start by factoring the polynomial with any of the factoring methods seen above. If we have a sum of perfect cubes, we use the formula $latex {{a}^3}+{{b}^3}=(a+b)({{a}^2}-ab+{{b}^2})$.

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Factoring Cubic Polynomials

So you can't always factor a third degree polynomial by grouping but sometimes you can so it's good to look for it. So when we see it written like this, we say okay, x to the third minus four x squared, is there a common factor here? Well, yeah
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How to Factor a Cubic Polynomial: 12 Steps (with Pictures)

Factor a Third Degree Polynomial x^3 - 5x^2 + 2x + 8. This video shows you how to factor a third degree polynomial.
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Factoring higher degree polynomials (video)

It can be written in the following way: ( a x 2 + b x + c) ⋅ ( d x + e) ( a, b, c, d, e ∈ Z) with { a ⋅ d = 36 = 2 2 ⋅ 3 2 a ⋅ e + b ⋅ d = 0 b ⋅ e + c ⋅ d = − 127 c ⋅ e = 91 = 7 ⋅ 13 How do I proceed from here?

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