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goes into times so you have:

Subtract the result from the dividend:

Now repeat the process:

, the largest degree term of your divisor, goes into - ... -3 times so you have:

Subtract the result from :

3y^2 is of greater degree than -y so -y is the remainder.

The quotient is y-3 and the remainder is -y

Check using:

Dividend = quotient * divisor + remainder

Remainder theorem:

If you divide a polynomial p(x) by a factor (x-a), the remainder is p(a). In plain English: the remainder is the y-value you get if you evaluate the polynomial at x=a.

example:

If you divide by , the remainder is , which is . Note that we can conclude about the remainder without knowing the quotient.

I hope this helps.

Good luck!