Question

On dividing x cube-3x^2+x+2 by a polynomial g(x),the quotient and remainder are x^2-2&-2x+4.find g(x)

Answer 1

On dividing x3 – 3x2 + x + 2 by a polynomialg(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

Answer 2

this is your answer of this question.