Factoring Quadratic Polynomials by hand is a good skill to have, but sometimes it’s just annoying. There’s no builtin function for factoring, but with a little programming knowledge you can recreate the quadratic formula on your TI84 which will give you the 2 solutions.
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Or use this code for reference:

prompt A,B,C
(B^24AC)→D
((B+sqrt(D))/(2A))→E
((Bsqrt(D))/(2A))→F
Disp E,F

I usually leave it in "real" mode, that way it gives an error when the discriminant is less than 0, and you know you have to change the mode to complex and get the imaginary solutions.
It works for most equations, but there are a few exceptions
1) If the discriminant is not a perfect square, then you might get a long decimal or fraction, like: x^2+2x5
2) If the coefficient on x^2 is greater than 1, it will be hard to reverse engineer the factored form because it will just give you the actual x solution. 2x^211x21=(2x+3)(x7) But the program shows x=7 & x=1.5
3) If it’s a complex solution with a long decimal that doesn’t fit on the screen