Question

on dividing x^3-3x^2+x+2 by a polynomial g+x) the quotient and remainder are x-2 and -2x+4 respectively find g(x)

Answer 1

Hii friend,

P(X) = X³-3X²+X+2

R(X) = -2X+4

Q(X) = X-2

G(X) = ?

we know that,

P(X) = G(X) × Q(X) + R(X)

G(X) × Q(X) = P(X) - R(X)

= X³-3X²+X+2 - (-2X+4)

= X³-3X²+X+2 +2X-4

= X³-3X²+3X-2

G(X) × Q(X) = X³-3X²+3X-2

G(X) × (X-2) = X³-3X²+3X-2

G(X) = (X³-3X²+3X+2)÷(X-2)

On dividing X³-3X²+3X+3 by X-2 we get,

G(X) = X²-X+1



HOPE IT HELPS!!!!!