FACTORISE (x+1)(x+2)(x+3)(x+4)-3

Asked by Anand | 3rd Sep, 2016, 10:44: PM

Expert Answer:

begin mathsize 14px style left parenthesis x plus 1 right parenthesis left parenthesis x plus 2 right parenthesis left parenthesis x plus 3 right parenthesis left parenthesis x plus 4 right parenthesis minus 3 equals 0
rightwards double arrow left square bracket left parenthesis x plus 1 right parenthesis left parenthesis x plus 4 right parenthesis right square bracket left square bracket left parenthesis x plus 2 right parenthesis left parenthesis x plus 3 right parenthesis right square bracket minus 3 equals 0
rightwards double arrow left parenthesis x squared plus 5 x plus 4 right parenthesis left parenthesis x squared plus 5 x plus 6 right parenthesis minus 3 equals 0
L e t space x squared plus 5 x equals a
rightwards double arrow left parenthesis a plus 4 right parenthesis left parenthesis a plus 6 right parenthesis minus 3 equals 0
rightwards double arrow a squared plus 10 a plus 24 minus 3 equals 0
rightwards double arrow a squared plus 10 a plus 21 equals 0
rightwards double arrow a squared plus 7 a plus 3 a plus 21 equals 0
rightwards double arrow a left parenthesis a plus 7 right parenthesis plus 3 left parenthesis a plus 7 right parenthesis equals 0
rightwards double arrow left parenthesis a plus 7 right parenthesis left parenthesis a plus 3 right parenthesis equals 0
rightwards double arrow a equals negative 7 space o r space a equals negative 3
rightwards double arrow x squared plus 5 x equals negative 7 space o r space x squared plus 5 x equals negative 3
rightwards double arrow x squared plus 5 x plus 7 equals 0 space o r space x squared plus 5 x plus 3 equals 0
C o n s i d e r space x squared plus 5 x plus 7 equals 0
D i s c r i m i n a n t space equals D space equals space left parenthesis 5 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 7 right parenthesis equals 25 minus 28 equals negative 3 less than 0
H e n c e comma space i t space c a n n o t space b e space f a c t o r i s e d.
C o n s i d e r space x squared plus 5 x plus 3 equals 0
B y space Q u a d r a t i c space f o r m u l a comma
x equals fraction numerator negative 5 plus-or-minus square root of 5 squared minus 4 left parenthesis 1 right parenthesis left parenthesis 3 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction equals fraction numerator negative 5 plus-or-minus square root of 13 over denominator 2 end fraction
T h u s comma space f a c t o r s space a r e space open parentheses x minus open parentheses fraction numerator negative 5 plus square root of 13 over denominator 2 end fraction close parentheses close parentheses open parentheses x minus open parentheses fraction numerator negative 5 minus square root of 13 over denominator 2 end fraction close parentheses close parentheses end style

Answered by Rashmi Khot | 6th Sep, 2016, 09:06: AM