Question

Factorize
(x+1)(x+2)(x+3)(x+6)-3x^2

Answer 1

carefully expand to get
x^4+12x^3+47x^2+72x+36 - 3x^2
= x^4 + 12x^3 + 44x^2 + 72x + 36

I assume it will factor, (or else why have the question?)
I tried all possible factors of 36, and none made the expression zero, so there are no binary factors with rational numbers.

I then assumed we had something like
(x^2 + bx + c)(x^2 + dx + e), expanded that , then compared coefficients.
solving these 4 equations in 4 unknowns gave me
b= 4
c = 6
d = 8
e = 6

for:

(x^2 + 4x + 6)(x^2 + 8x + 6)

Nasty question.

Answer 2

Nice solution i was very bore due to this ques

Answer 3

I am not happy to learn that I went through the effort of solving the question to relieve your boredom.