Question

Divide x3-6x2+11x-6 by x2-5x+6 and write the quotient and remainder​

Answer 1

Let f(x)=x

3

−6x

2

+11x−6

and p(x)=x−2

Dividing f(x) by p(x) we get

Quotient q(x)=x

2

−4x+3 and Remainder r(x)=0

p(x)q(x)=(x−2)(x

2

−4x+3)

p(x)q(x)=x

3

−4x

2

+3x−2x

2

+8x−6

p(x)q(x)=x

3

−6x

2

+11x−6

⇒p(x)q(x)=f(x)

⇒p(x)q(x)+0=f(x)

⇒p(x)q(x)+r(x)=f(x)

Hence division algorithm verified