How do you divide #(x^101+x+1 ) / (2x+1)
# using polynomial long division?

Question

How do you divide #(x^101+x+1 ) / (2x+1) 
# using polynomial long division?

Eva Abramson · Accepted Answer

See example

Here is an example of how to do it:

Julia Adams · Answer

undefined To divide (x^101+x+1) by (2x+1) using polynomial long division, follow these steps:

1. Start by dividing the highest degree term of the numerator (x^101) by the highest degree term of the denominator (2x). The result is (1/2)x^100.

2. Multiply the entire denominator (2x+1) by the result obtained in step 1, which is (1/2)x^100. This gives you (1/2)x^101 + (1/2)x.

3. Subtract the result obtained in step 2 from the numerator (x^101+x+1). This can be done by changing the signs and combining like terms. The subtraction gives you (1/2)x + 1.

4. Bring down the next term from the numerator, which is 1.

5. Divide the term brought down (1) by the highest degree term of the denominator (2x). The result is (1/2).

6. Multiply the entire denominator (2x+1) by the result obtained in step 5, which is (1/2). This gives you (1/2)x + (1/2).

7. Subtract the result obtained in step 6 from the result obtained in step 4. This can be done by changing the signs and combining like terms. The subtraction gives you 1 - (1/2)x.

8. Since there are no more terms left in the numerator, the division is complete.

The final result of the division is (1/2)x^100 + (1/2)x + (1/2) with a remainder of 1 - (1/2)x.

How do you divide #(x^101+x+1 ) / (2x+1) # using polynomial long division?