Question

Write the remainder and quotient of (x3-6x2+11x-6) by (x2-5x+6)

Answer 1

Step-by-step explanation:

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)

Answer 2

Answer:

x^2-5x+6)x^3-6x^2+ 11x -6( x -1

x^3-5x ^2+ 6x

- + -

______________

-x^2 + 5x -6

-x^2 +5x -6

+ - +

_____________

0

remainder = 0

quotient = x-1