Question

Divide x - 6x² + 11x - 6 by x-1 and verify with Division Algorithm ?​

Answer 1

Answer:

p(x) = x³ - 6x² + 11x -6 

g(x) = x +2 

Let q(x) = ax² + bx +c

Let r(x) = k

acc. to division algorithm

p(x) = g(x) * q(x) + r(x)

x³ - 6x² + 11x -6 = (x +2) * (ax² + bx +c) + k

x³ - 6x² + 11x -6 = ax³ + bx² +cx +2ax² +2bx +2c + k

x³ - 6x² + 11x -6 = ax³ + bx² +2ax² +2bx +cx +2c + k

x³ - 6x² + 11x -6 = ax³ + (b +2a)x² +(2b +c)x +2c + k

Equating the equation of like powers of x on both sides , we get

on equating the cofficients of x³ 

1 = a

on equating the cofficients of x²

-6 = 2a +b 

-6 = 2 + b

-6 -2 =b

-8 = b

on equating the cofficients of x

11 = 2b +c

11 = -16 +c

11 + 16 = c 

27 = c

on equating the constant term

-6 = 2c +k

-6 = 54 +k

-6 - 54 = k

-60 = k

solving these equation we get

a = 1

b = -8

c =27 

k =-60

q(x) = x² -8x + 27

reminder = -60

Answer 2

:

Division algorithm is a=bq+r where 0<=r<b