Can the degree of remainder be greater than the quotient?

The remainder is always less than the divisor. If the remainder is greater than the divisor, it means that the division is incomplete. It can be greater than or lesser than the quotient. For example; when 41 is divided by 7, the quotient is 5 and the remainder is 6.

Can a remainder be bigger than the number you are dividing by?

A remainder can never be larger than the number you are dividing by (divisor). Even if you are dividing a number by fifty-one (51), you can’t have a remainder greater than or equal to fifty-one.

Could the remainder ever have the same degree as the divisor or a higher degree?

No. The condition on the remainder r is that r=0 or degr

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.

How do you find the degree of the quotient and remainder?

In general, if we divide a polynomial of degree n by a polynomial of degree 1, then the degree of the quotient will be n − 1. And the remainder will be a number. x3 − 8×2 + x + 2 by x − 7. P(x) = Q(x)· D(x) + R.

Why can’t the remainder be bigger 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.

What is the degree of the remainder?

The degree of the remainder is less than the degree of the divisor, by definition of polynomial division. and collect the terms of the same degree. We get 8×4+3x−1=2Ax4+2Bx3+(A+2C)x2+(B+D)x+C+E.

How would you compare the degree of the dividend and the degree of the quotient when the divisor is linear of degree one?

The degree of the quotient is one less than the degree of the dividend. For example, if the degree of the dividend is 4, then the degree of the quotient is 3.

What is the degree of a remainder?

When a polynomial is divided by x−c, the remainder is either 0 or has degree less than the degree of x−c. Since x−c is degree 1, the degree of the remainder must be 0, which means the remainder is a constant.

Why the remainder is always less than the divisor?

Explanation: 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.

What is the degree of the remainder of the quotient?

If the degree of the remainder is larger than the degree of the quotient, then the degree of the divisor is at least (half of the degree of the dividend) plus one. However, the converse is not necessarily true. The degree of the quotient is equal to the degree of the dividend minus the degree of the divisor.

How big can the quotient of a polynomial be?

The quotient can be arbitrarily large. Similarly for polynomials. The quotient can be as big (in degree) as it wants. Given some remainder r of degree less than deg ( a), the polynomial q ( x) a ( x) + r ( x) has quotient q under division by a – where q can be any polynomial, even of degree thirty eight trillion.

How do you find the remainder of a linear polynomial?

Let p (x) be any polynomial of degree greater than or equal to one and let ‘a’ be any real number. If p (x) is divided by the linear polynomial (x – a), then the remainder is p (a). Proof: p (x) is a polynomial with degree greater than or equal to one. It is divided by a polynomial (x – a), where ‘a’ is a real number.

How to prove the remainder theorem?

We see that when a polynomial p (x) of a degree greater than or equal to one is divided by a linear polynomial (x – a), where a is a real number, then the remainder is r which is also equal to p (a). This proves the Remainder Theorem. For example, check whether the polynomial q (t) = 4t 3 + 4t 2 – t – 1 is a multiple of 2t+1.