What is the smallest positive integer $n$ such that $\sqrt{n} - \sqrt{n-1} < 0.01?$

x^2 + 10x + 38 + 161/x-4

to find this, you'll need to synthetically divide using synthetic division.

here's how you would set it up:

4 is what you're dividing by (set x -4 = 0)

the numbers you are 'dividing' by are 1, 6, -2, and 9 or the coefficients of the terms listed above.

bring the first term down (1), multiply that by 4 before raising it to the next term to add (6). repeat this process as so:

6 + 4 = 10; 10 x 4 = 40; 40 - 2 = 38 x 4 = 152 + 9 = 161

161 is over x-4 as there are now two constants and you cannot combine them.

also, i'm not sure if it was -9 or +9, so i assumed.

hope this !