Question

on dividing the polynomial px= x3-3x2+x+2 by a polynomial gx, the quotient qx and remainder rx are x-2 and - 2x+4 respectively find the polynomial gx

Answer 1

here is your answer......

hope this will help you out

Answer 2

Hii friend,

P(X) = X³-3X²+X+2

Q(X) = X-2

R(X) = -2X+4

G(X) = ?

By Euclid division lemma,

Dividend = Divisor × Quotient + Remainder

X³-3X²+X+2 = G(X) × (X-2) + (-2X+4)

G(X) = F(X) - R(X)/Q(X)

Now,

F(X) - R(X) = X³-3X²+X+2 - (-2X+4)

= (X³-3X²+3X-2)

Therefore,

G(X) = (X³-3X²+3X-2)/(X-2)

We have to divide (X³-3X²+3X-2) by( X-2), we get G(X) = (X²-X+1).


HENCE,

G(X) = (X²-X+1).

HOPE IT WILL HELP YOU.... :-)