Table of Contents
- 1 Why does the remainder have to be less than the divisor?
- 2 Can degree of remainder and divisor be same?
- 3 Is degree of remainder always 1 less than degree of divisor?
- 4 Is degree of remainder less than degree of quotient?
- 5 Is dividend is always greater than the divisor?
- 6 Why is the quotient greater than 1?
- 7 What is a remainder theorem?
- 8 What is the Order of the remainder of the divisor?
Why does the remainder have to be less than the divisor?
If a remainder is more than divisor, latter can go one more time and hence division is not complete. Even if remainder is equal to divisor, it can still go one more time. Hence remainder has to be less than the divisor.
Can degree of remainder and divisor be same?
Degree of remainder is always less than the degree of divisor as if remainder is greater than divisor than the number to be divided can be divided again by adding remainder. When divisor completely do not divide dividend we get remainder whose degree is always tried to be kept minimum whole number.
Does the remainder have to be smaller in polynomial division?
In polynomial division, the remainder’s degree is always less than that of the divisor, but when dividing x3+y3 by x+5, it isn’t.
What is always less than the divisor?
When one number divides another number completely, the remainder is 0. The remainder is always less than the divisor. For example; when 41 is divided by 7, the quotient is 5 and the remainder is 6.
Is degree of remainder always 1 less than degree of divisor?
No, the remainder can be any order from 0 to one degree less. The remainder will be the zero polynomial if the divisor divides exactly.
Is degree of remainder less than degree of quotient?
The degree of the quotient is equal to the degree of the dividend minus the degree of the divisor. The degree of the remainder must be less than the degree of the divisor.
Can remainder be negative in polynomials?
You can write the remainder using the symbol R, or as a fraction added to the rest of the quotient with the remainder in the numerator and the divisor in the denominator. In this case, since the remainder is negative, you can also subtract the opposite. Correct. The correct answer is x – 3 – .
Can the remainder of a polynomial division be negative?
What do you mean with “negative”? Anyway, whatever it is, the answer is yes: any polynomial can be remainder of a division, with the only condition that it is of degree smaller that the dividend and the divisor.
Is dividend is always greater than the divisor?
Solution: Know that, Now, we can say that the dividend is greater than the divisor. Hence, “dividend is always greater than the divisor” is True.
Why is the quotient greater than 1?
When the divisor is smaller than the dividend, the quotient is more than 1. Another example where the divisor smaller than the dividend. When the divisor is the same size as the dividend, the quotient is 1. When the divisor is larger than the dividend, the quotient is less than 1.
Are the remainders always polynomials of degree 0?
In the case of linear polynomials as divisors, we can therefore conclude that the remainders will always be polynomials of degree 0, that is, constants.
Should the degree of the remainder be greater or less than divisor?
If you are still not convinced that the degree of the remainder should be less than that of the divisor, try to think of a scenario where the remainder has a degree greater than that of the divisor, and then observe that the remainder itself can be further divided by the divisor, which defeats the whole purpose of it being a remainder.
What is a remainder theorem?
A Remainder Theorem is an approach of Euclidean division of polynomials. “It is applied to factorize polynomials of each degree in swift and elegant manner. Theorem implies that after you divide a polynomial P (x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
What is the Order of the remainder of the divisor?
The order of the divisor is 3. The order of the remainder is 0. By the way, with long division of simple large numbers, a divisor of 4,321 could have remainders of 9 or less, 99 or less, 999 or less or any other number less than 4321. Why should the remainder not be greater than the divisor?