How you find the factors depends a lot on what tools you have in your mathematical toolbox.
Note on terminology, although there is a "quartet" of terms, the word "quartic" refers to the degree being 4. Not to the number of terms. We could call it a quadrinomial, but I don't hear that or see it in textbooks.
To factor a cubic polynomial, First check for common factors and check for sum or difference of two cubes. (Not relevant in this problem.)
I would then try factoring by grouping . It won't always work, but it doesn't take long to try it:
You may have noticed that both the first and last terms are perfect cubes. If so, you might try using the guess
Or, you might use the rational zero theorem to learn that
Which can be further factored to get: