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factorize (x+1)(x+2)(x+3)(x+6)-3x 2

factorize


(x+1)(x+2)(x+3)(x+6)-3x2

Grade:10

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question

f(x) = (x+1)(x+2)(x+3)(x+6) - 3x^2
f(x) = (x^2+4x+6)(x^2+8x+6)
f(x) = (x^2+4x+6)(x^2+4x+4x+6)
Use simple quadratic formulas now
f(x) = -(x+\sqrt{10}+4)(-ix+\sqrt{2}-2i)(ix+\sqrt{2}+2i)(-x+\sqrt{10}-4)
mycroft holmes
272 Points
9 years ago
Given expression equals 
 
Now we have  
 
Hence if ,
 
the given expression can be written out as AB-6A+3B-18 = (A+3)(B-6)
 
which on substituting back for A and B equals
 
 
Both expressions are irreducible over integers and hence you can leave the factorization at this stage
 
 
 
 

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