Question

Apply the division algorithm to find the quotient and remainder on dividing x3 - 6x2 + 11x - 6 by x+ 2

Answer 1

reminder 60
quotient is x²-8x+27
hope it help u...

Answer 2

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