Question

when x power 11 - 1 is divided by x + 1​

Answer 1

Answer:

0

Step-by-step explanation:

Since -1 is a root of x11+1 , x11+1 is divisible by x+1.

To expand a little the answer, and give it a bit more meat, the division of polynomials is pretty similar to the division of integers, and we can use basically the same algorithm.

Instead of looking at decimal digits, we look at the degrees. We are dividing a 11-degree polynomial by a 1-degree polynomial, so the first thing we need to find is the 10-degree term a10x10 that, when multiplied by (x+1) , matches the 11-degree term of x11+1. This is obviously x10 .

Now we proceed the same way we would with integers:

x11+1=x10∗(x+1)+R1. => R1=−x10+1

R1=−x10+1=−x9∗(x+1)+R2. => R2=x9+1

R2=x9+1=x8∗(x+1)+R3. => R3=−x8+1

now I think you guessed the pattern, and we can continue all the way down to

R10=x1+1=1∗(x+1)+R11. => R11=0

and, putting it all together:

x11+1=(x10−x9+x8−...+x2−x+1)∗(x+1)+0

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