Question

what is the remainder of 5x4 - 2x2 -3 by x-1

Answer 1

So what they are actually telling you is that when you divide f(x) by x-1 then what the R is.
There is a big way [THE LONG DIVISION] way but I'll tell you way shorter method.
We are given that
f(x) = 5x4 - 2x2 -3
Now when they say we have to divide by x-1 it actually means that the negative of -1 is the value of x!
For eg. Let's say if it said x+2, THEN -2 would have been the value of x :D
So now
as we're dividing by x-1, x=+1
so
f(1) = 5(1)^4 - 2(1)^2 -3 = 5-2-3 which is 0
So the Remainder is 0!
Hinting us that (x-1) is actually a perfect factor of f(x)
Btw f(x) is just a fancy way of writing that long polynomial! :D
Getting me? :)