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.

Table of Contents

### 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.

### When you perform long division of polynomials Why must the degree of the remainder be less than the degree of the divisor?

When the remainder is 0 ,division is completed. when the remainder is greater than the divisor, division must continue, hence,the remainder must be less than the divisor.

### What is the rule of remainder?

In other words, the remainder is equal to the value of a(x) when x is equal to k. Precisely what we stumbled upon! This is exactly what the remainder theorem is: When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x equal to k, the remainder is given by r=a(k).

### How does the quotient compared to the dividend when the divisor is less than 1?

When the divisor is less than 1, the quotient is larger than the dividend. Decreasing the divisor to 1/2 increases the quotient to 10 1/2 . When the divisor is smaller than the dividend, the quotient is more than 1.

### What is the difference between quotient and remainder?

The remainder is the number left over after dividing one number by another. The quotient is the quantity produced by the long division of two numbers.

### Does the remainder have to be smaller in polynomial division?

You know, from long division of regular numbers, that your remainder (if there is one) has to be smaller than whatever you divided by. In polynomial terms, since we’re dividing by a linear factor (that is, a factor in which the degree on x is just an understood “1”), then the remainder must be a constant value.

### Why is long division of polynomials important?

Thus long division is a means for testing whether one polynomial has another as a factor, and, if it does, for factoring it out. For example, if a root r of A is known, it can be factored out by dividing A by (x – r).

### Why is the remainder theorem true?

The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x – a, the remainder of that division will be equivalent to f(a). … It should be noted that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x – number.

### Is remainder always less than divisor?

The remainder is always less than the divisor. If the remainder is greater than the divisor, it means that the division is incomplete. … For example

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