My class has just been taught about polynomial division, and how it can be used to see if something is a factor (although remainder theorem is quicker), if the remainder = 0.
But what is the use of remainder that does not equal 0, I'm unsure where to apply this to in situations.
For example if you do:
the remainder is $50$, which means (more on the graphic side of things), that the line $x=2$ will intercept $3x^3+5x^2+x+4$ at $(2,50)$
But what use is this beyond "find the intercept", "find the remainder"?
(Like how you can ask "5 - 0.2 = ?", but a situation you apply that to, could be: "what is the change from a £5 note used to buy a 20p pencil")