how to factorise x^4+4x^3-x^2-16x-12using long division method

Asked by Anishma Joseph | 2nd Jul, 2013, 10:47: PM

Expert Answer:

Let f(x)=  x^4+4x^3-x^2-16x-12
Clearly, (x+1), (x+2) are factors of of f(x). (Since, f(-1)=f(-2)=0)
Hence, (x+1).(x+2)=x^2+3x+2 is a factor of f(x).
 
Now, divide f(x) by x^2+3x+2.
The remainder will be 0 and quotient will be x^2 + x - 6.
Now, x^2 + x - 6 = (x+3)(x-2)
 
Hence, f(x) = (x+1) (x+2) (x+3) (x-2)

Answered by  | 2nd Jul, 2013, 11:08: PM

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