Algebraic equations - factoring cubic and degree four expressions

I'm practicing for an entry exam to a foreign university and one of the requirements is understanding

"Algebraic equations - factoring cubic and degree four expressions"

Could someone give me an example of this? I feel like the english is off. I have not had an issue understanding any of the previous questions.. thanks.

• For example, how would you factor the expression $x^3+3x^2+3x+1$? In general, one may need to solve the cubic or quartic, but a general understanding would be spotting patterns between coefficients and playing with polynomials, so factorization can be done by observation. On that note, you are applying for an undergraduate course, I presume? Commented Mar 7, 2017 at 4:17
• Yes, going for computer science :) Commented Mar 7, 2017 at 4:18
• Well, do not trust me completely, I only turned 13 a few months back. Have you managed to factorize the given expression? Commented Mar 7, 2017 at 4:21
• I'm reviewing it in khan academy now.. this looks to be Algebra I not Algebra II level? Commented Mar 7, 2017 at 4:25
• @астонвіллаолофмэллбэрг we trust Olof Mellberg completely Commented Mar 7, 2017 at 4:26

factor $$x^4 + 9x^2 + 4x + 21$$ The central parts are the rational roots theorem, how do divide out if there is a root, and the Gauss theorem on content, which says that a polynomial with integer coefficients that factors with rational coefficients ALSO factors with all integer coefficients.