Question

find the remainder of X=0​

Answer 1

Answer:

no reminder because any no divided by zero is zero

Answer 2

Answer:

Find the remainder when x

100

is divided by x

2

−3x+2.

Answer

As per the reminder theory for any

polynomial equation

p(x)=g(x).q(x)+r(x)→(i)

where p(x),g(x)= polynomials

q(x)= quotient

r(x)= reminder

Assuming r(x)=Ax+B

here p(x)=x

100

,g(x)=x

2

−3x+2

Simplifying g(x)

g(x)=x

2

−3x+2

=x

2

−2x−x+2

=(x−2)(x−1)

Substituting in eq

n

(i)

p(x)=(x−2)(x−1).q(x)+Ax+B

taking (x)=1

p(1)=(1−2)(1−1).q(1)+A(1)+B

1

100

=0+A+B

A+B=1→(i)

taking x=2

p(2)=(2−2)(2−1).q(x)+A(2)+B

2

100

=0+2A+B

2A+B=2

100

→(ii)

from eq

n

(i) B=1−A putting it in eq

n

(i)

2A+1−A=2

100

A=2

100

−1

now B=1−2

100

+1=2−2

100

∴B(2−2

100

)

∴ Reminder =Ax+B

=(2

100

−1)−x+(2−2

100

)