yesFind the quotient and remainder when P(x)=2x^4+3x^3-x^2+5x-6 is divided by x^2+x-2.

Answer:

Quotient=2x^2+x+2

Remainder=5x-2

Is the answers right?

But these are equal. Think about what you mean when you say "2 remain -2". You mean . This is the same as 3.When x=0,

P(0)=-6

D(0)=-2

Q(0)=2

R(0)=-2

(-6)/(-2)

=3 remain 0

≠2 remain -2

6 remain 1 is wrong. .=6 remain 1

≠3 remain -7

It should be 6 remain -1 or 7 remain 1, both of which are the same as 3 remain -7.

You have here . It is entirely understandable to find this weird, but when you deal with infinities you get this kind of stuff.When x= 1,

P(1)=3

D(1)=0

Q(1)=5

R(1)=3

(3)/(0)

=undefined

≠5 remain 3

I think the main issue here is understanding what the quotient and remainder actually are. What you discovered at the very start was that

This is not contradicted by any substitution for x although things get weird if the divisor is 0.