HOW do you divide x3 - 7x plus 6 by x-2?

Answer 1

This can be done using long division. That's rather hard to depict here though, so to run through it verbally:

Take (x - 2) and multiply it by a factor that gives us the term (x3 - 2). That factor would be x2, making that term (x3 - 2x2). Subtract that result from our initial equation. This gives us:

-2x2 - 7x + 6

Now repeat that process, finding a factor by which to multiply (x - 2) which will give us a term that is equal to the first term of our new expression. That factor would be -2x, giving us (-2x2 + 4x). Again subtract it from our equation, and we get:

-11x + 6

Again we repeat, this time multiplying our divisor by -11, giving us (-11x + 22). Subtract it, and we get:

-16

And that's our remainder, as we're now out of terms. Now we add up the terms and we get:

x2 - 2x - 11, with a remainder of -16. That could be expressed as:
x2 - 2x - 11 - 16 / (x - 2)