I need help understanding how to divide a polynomial, somethings just not clicking for me. Can you please help me understand this problem so I can understand the future ones? Thank you.

There are two ways to divide polynomials : long division and synthetic division.
please follow my picture as i explain !

1. divide the p from p+6 to 3p^2. it goes in 3p times. write it above the 20p.
2. multiply p+6 by 3p and write.
3. subtract 3p^2+20p and 3p^2+18p.
4. bring down the +11

and repeat the steps!

AND ALSO! if you happen to have missing terms, (ex. x^6+2x^4+6x-9; you’re missing a ^5, ^3, ^2 term,) then you can put a ‘0’ in front of them and start your dividing process.

synthetic division is easier.
you have to change your sign to put in the box.

1. change your sign.
2. write ONLY your coefficients.
3. bring down your first coefficient. (in this case 3)
3. multiply your boxed number (-6) and your first coefficient (3) and write it below your next coefficient.
4. add your next coefficient and the number you just wrote down.

and you repeat!

again, if you have missing terms, you can write 0s in their place.

hope this helped! :) i’m really sorry for my bad handwriting :(

Istg idk..if there all the same length there all the same number but use google