Division by 0 is undefined. Not sure how it will be marked even though the final answer is valid.

Brother i am using remainder theorem. It is not really division. Let alone divided by 0. ?

I know you're doing polynomial long division. I can see that in principle it is the correct method.

What I'm referring to is the fact that the question has defined/given that 2x² + x - 8 = 0

So strictly speaking,

When we are dividing 2x³ + 17x² + 123 by 2x² + x - 8 , we are dividing by 0. And division by 0 is undefined.

If I were the teacher I would mark this correct, but I'm not sure what the perspective of the student's marker/teacher will be.


Eg. Something along the lines of 187 × 0 = 0, but we can only say that 0/187 = 0 and not 187/0 = 0 or 0/0 = 187.

That's why I decided not to go with this approach, but the other one instead.

i.e

2x² + x - 8 = 0

2x² + x = 8 ①

2x² = 8 - x

Multiply both sides by x,

2x³ = 8x - x² ②


Then,

2x³ + 17x² + 123

= 8x - x² + 17x² + 123 (sub in ②)

= 16x² + 8x + 123

= 8(2x² + x) + 123

= 8(8) + 123 (sub in ①)

= 64 + 123

= 187

Ha ha. Under factorization, one method of obtaining the other factor is DIVIDE the dividend by the first factor found. This is the same. Furthermore, long division is a technique used in factorization and remainder theorem. Anyway, i do not need to convince you. Continue what you believe in. Be happy.

Of course I know that. But that is for the general case when no values are defined yet.

Eg. Divide 2x³ + 17x² + 123 by 2x² + x - 8 , where neither is equated to anything.

I also said if I were the marker, I would mark your working as right so of course I'm not against it.

Of course we all know long division is commonly used here.

I never said you were wrong, btw. And no, I'm not trying to convince you or anything and I can see your perspective (which I shared as well originally until I realised this point). I'm just interested to hear the marker's perspective.

So chill a bit yea.