Remainder of polynomial division

In summary, if the remainder of f(x)/g(x) is a (where a is constant), then the remainder of (f(x))n/g(x) is an. This can be verified by raising both sides of the equation to the power of n and using the binomial theorem. Several examples have been tested and the result is proven to be correct.
  • #1
songoku
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Is this true?

If the remainder of f(x) / g(x) is a (where a is constant), then the remainder of (f(x))n / g(x) is an

I don't know how to be sure whether it is correct or wrong. I just did several examples and it works.

Thanks
 
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  • #2
songoku said:
Is this true?

If the remainder of f(x) / g(x) is a (where a is constant), then the remainder of (f(x))n / g(x) is an

I don't know how to be sure whether it is correct or wrong. I just did several examples and it works.

Thanks
One way to deal with remainders is to write down what it means, which is always a good point to start at.
Here you have ##f(x)=q(x)\cdot g(x) + a##. Now you can work with it.
 
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  • #4
I tried it and found out it is actually correct.

Thanks a lot for the help
 

1. What is the concept of "remainder" in polynomial division?

The remainder in polynomial division refers to the number or expression that is left over after dividing one polynomial by another. In other words, it is the part of the dividend that cannot be evenly divided by the divisor.

2. How is the remainder calculated in polynomial division?

The remainder is calculated by dividing the dividend by the divisor and then subtracting the product of the quotient and the divisor from the dividend. The resulting number or expression is the remainder.

3. Can the remainder in polynomial division be negative?

Yes, the remainder in polynomial division can be negative. This can happen when the dividend is smaller than the divisor or when the signs of the dividend and divisor are different.

4. What is the significance of the remainder in polynomial division?

The remainder in polynomial division is significant because it helps us determine if the polynomial is evenly divisible by another polynomial. If the remainder is zero, then the polynomial is evenly divisible, but if the remainder is not zero, then the polynomial is not evenly divisible.

5. How can the remainder in polynomial division be used in real-life applications?

The concept of remainder in polynomial division can be used in various real-life applications, such as calculating the interest on a loan or dividing resources among a group of people. It can also be used in coding and computer science to determine if a number is prime or to solve problems in cryptography.

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