Question

divide 5x^3-13x^2+21x-14 by 3-2x+x^2 and verify by euclids division algorithm​

Answer 1

Given f(x) = 5x^3 - 13x^2 + 21x - 14.

Given g(x) = 3 - 2x + x^2.

We need to divide f(x) by g(x).


                            5x - 3
                          ---------------------------------
= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14

                           5x^3 - 10x^2 + 15x

                           ---------------------------------

                                       -3x^2 + 6x - 14

                                       - 3x^2 + 6x - 9

                            -----------------------------------
-5.

Here,

Dividend = 5x^3 - 13x^2 + 21x - 14

Divisor = 3 - 2x + x^2

Quotient = 5x - 3

Remainder = -5


Division Algorithm:

Dividend = Divisor * Quotient + Remainder

  = (3 - 2x + x^2) * (5x - 3) + (-5)

                 = 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5

                 = 5x^3 - 13x^2 + 21x - 14.


LHS = RHS



Hope this helps!