How do you do long division of polynomials with remainders?

Question

Hazel Anglin · Accepted Answer

It is the same but just instead of getting 0 you get a polynomial in the last step.

Divide # 3x^3 – 5x^2 + 10x – 3 # by # 3x + 1#

in this case you get a polynomial seven which can be writtten in algebraic terms as #7x^0#
so this can be proved using the division algoritm

dividend = divisor #*# quotient + remainder

Julia Adams · Answer

undefined To perform long division of polynomials with remainders, follow these steps:

1. Arrange the dividend (the polynomial being divided) and the divisor (the polynomial dividing the dividend) in descending order of degree.
2. Divide the first term of the dividend by the first term of the divisor to obtain the first term of the quotient.
3. Multiply the entire divisor by the first term of the quotient.
4. Subtract the result obtained in step 3 from the dividend.
5. Bring down the next term of the dividend.
6. Repeat steps 2-5 until all terms of the dividend have been processed.
7. The final result is the quotient, and any remaining terms after the division process are the remainder.

Note: It is important to ensure that the terms are aligned correctly during each step of the process.