Sunday, March 31, 2013

On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x–2 and –2x+4, respectively. Find g(x).

On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x–2 and –2x+4, respectively. Find g(x).
according to division algorithm
Dividend = Divisor × Quotient+ Remainder
p(x)         = g(x)      × q(x)          + r(x),
plug the value in formula we get
x3 – 3x2 + x + 2 = g(x) *(x-2)   - 2x + 4
Add 2x and subtract 4 both side we get
x3 – 3x2 + x + 2 + 2x – 4 = g(x) *(x-2)
simplify and divide by x/2 we get
(x2 – 3x2 + 3x– 2)/(x-2) = g(x)


 So we get g(x)  = x2 – x +1

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