x4+x3-7x2-x+6

Asked by Cyrus Samion | 10th Jun, 2013, 10:35: PM

Expert Answer:

f(x) = x^4+x^3-7x^2-x+6 
f(x) = x^3(x+1) - (7x^2+ x -6)
f(x) = x^3(x+1) - (7x^2+ 7x-6x -6)
f(x) = x^3(x+1) - (7x-6)(x+1)
f(x) = (x+1) (x^3-7x+6)
 
By using remainder theorem for (x^3-7x+6)
f(1) = 1-7+6 = 0 Hence(x-1) is a factor of (x^3-7x+6)
Hence using long division method, we can get that f(x) =(x+1)(x-1)(x^2+x-6)
 
f(x) = (x+1) (x-1)(x^2+x-6)
f(x) = (x+1) (x-1) (x+3)(x-2)
 

Answered by  | 10th Jun, 2013, 10:57: PM

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