Question

factorise: (x+1)(x+2)(x+3)(x+4)-3. pls any1

Answer 1

logic to arrange1+4=2+3
=(x+1)(x+4)(x+2)(x+3)-3
=(x²+x+4x+4)(x²+2x+3x+6)-3
=(x²+5x+4)(x²+5x+6)-3

let y=x²+5x .......................... 1
=(y+4)(y+6)-3 
=y²+4y+6y+24-3
=y²+10y+21

factorization
=y²+3y+7y+21
=y(y+3)+7(y+3)
=(y+3)(y+7)
y= -3 or y= -7

put y= -3 in 1
-3=x²+5x
x²+5x+3=0 .......... a
put y= -7 in 1
-7=x²+5x
x²+5x+7=0 ........... b
solve a & b by Quadratic formula

x=(-5+√13)/2 , (-5-√13)/2
x= -5/2+√3i/2 , -5/2-√3i/2