Question

on dividibg x^3+3x+2 by a polynomial g(x), the quotient and thr remainder are x-2 and 16 respectively . find g(x)

Answer 1

☜☆☞hey friend ☜☆☞

here is your answer ☞
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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

(x³- 3x² + 3x– 2)/(x-2) = g(x)

So we get g(x) = (x²–x +1)


hope it will help you

Devil_king ▄︻̷̿┻̿═━一