Question

factorise:(x+1)(x+2)(x+3)(x+4)-3 brainly

Answer 1

Answer:

Given,

==>(x+1) (x+2) (x+3) (x+4) -3=0

==>{(x+1)(x+4)}{(x+2)(x+3)}-3=0

==>(x²+5x+4) (x²+5x+6) -3=0

Let x²+5x be a. Then,

==>(a+4) (a+6) -3=0

==>(a²+10a+24)-3=0

==>a²+10a+21=0

==>a²+7a+3a+21=0

==>a(a+7) +3(a+7) =0

==>(a+7) (a+3) =0

==>a= -7 or a= -3

==>x²+5x= -7 or x²+5x= -3

==>x²+5x+7=0 or x²+5x+3=0

Consider: x²+5x+7=0 (x²=a, 5x=b, 7=c)

Discrimination=D=b²-4ac = [(5x) ²-4(x²) (7)]

=(25x²-28x²) = -3x²<0

So, it can't be factorise .

Consider,(x²+5x+3) =0

By using Quadratic Formula:

=> x = {-5±√5²-4(1) (3)}/2(1)

=>x = (-5±√13) /2

Then, the factors are:

{x-(√5+13) /2} {x-(√5-13) /2} [Ans]

Hope it's beneficial...

Answer 2

Step-by-step explanation:

(x+1) (x+2)(x+3) (x+4) --15

( x+1)(x+4) = x^2 +5x +4:

(x+2) (x+3) = x^2 +5x+6

Now let us put x^2 + 5x+4 = m

The given problem is in terms of m

m (m+2) --15

m^2 +2m --15

Factoriese

m^2 +5m --3m --15

m (m+5) -3 ( m+5)

(m +5) (m--3)

Now factoriise

m+5 = x^2+5x+4+5 = x^2+5x+9

m-3 = x^2+5x+4 --3 = x^2+5x+1

(x^2+5x+9) (x^2 +5x +1) are the factors