Part A: In what way is the algorithmic process the same for integers and polynomials?

Part B: In what way is the algorithmic process different for integers and polynomials?

Select one answer for Part A and one answer for Part B.
A: Polynomial long division and integer division are not the same at all.

A: When using polynomial long division, the same process of divide, multiply, and bring down applies, just like when dividing integers.

A: When using polynomial long division, the multiply, subtract, and bring down portion applies just like when dividing integers.

B: When using polynomial long division, polynomial terms are added, not subtracted like in integer division.

A: When using polynomial long division, the same process of divide, multiply, subtract, bring down applies, just like when dividing integers.

B: Polynomial long division uses powers of variables instead of place values used when dividing integers, and only the first term of the divisor is considered in the divide step.

B: Polynomial long division treats remainders differently than they are treated in integer long division.

B: Polynomial long division and integer division are completely the same.

B: Polynomial long division uses powers of variables instead of place values used when dividing integers, and only the first term of the divisor is considered in the divide step

Step-by-step explanation:

The above answers are pretty self-explanatory.

I find polynomial division easier, because the "trial division" step uses only the highest-degree terms, so always gives the exact result you need for the quotient. (There's no "guess and check" as with integer long division.) Powers of the variable take the place of powers of 10 (or whatever number base you're using) in integer long division.

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For integer long division, the steps are ...

Divide the leading portion of the dividend by the divisor to determine the quotient digit.
Multiply the divisor by the quotient digit and subtract the result from the dividend, paying attention to place value. If the quotient digit is too large (the difference is negative), choose a smaller value and repeat.
Append the next succeeding digit of the dividend to the difference from the above step to form the new dividend and repeat from the first step until the desired quotient precision is achieved.
If all given digits of the dividend have been exhausted, append zero to form the new dividend.
Any remainder can be expressed as a fraction with the divisor as its denominator. (That fraction is added to the rest of the quotient.)

For polynomial long division, the steps are similar.

Divide the highest degree term of the dividend by the highest-degree term of the divisor to form the next term of the quotient.
Multiply the quotient term just found by the divisor and subtract the result from the dividend to obtain the new dividend.
Repeat from the first step until the degree of the dividend is less than that of the divisor. If this remainder is non-zero, it can be expressed as a fraction with the divisor as its denominator. (That fraction is added to the rest of the quotient.)

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Examples of each are shown in the attachments.