## What is the quotient in polynomial long division?

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1).

### How do you find the remainder of a polynomial?

Important Notes

- When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k)
- The remainder theorem formula is: p(x) = (x-c)·q(x) + r(x).
- The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder.

#### How do you do the long division method?

Long Division Steps

- Step 1: Take the first digit of the dividend from the left.
- Step 2: Then divide it by the divisor and write the answer on top as the quotient.
- Step 3: Subtract the result from the digit and write the difference below.
- Step 4: Bring down the next digit of the dividend (if present).

**How do you find the quotient and remainder?**

Expressions used in program to calculate quotient and remainder: quotient = dividend / divisor; remainder = dividend % divisor; Note: The program will throw an ArithmeticException: / by zero when divided by 0. Program 2: For a negative number.

**What is quotient and remainder in division?**

Quotient – The resultant of the division is called the quotient. Remainder – The number that is left after division is called the remainder.

## How do you solve long polynomials?

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero. The solutions to the resulting equations are the solutions to the original. Not all polynomial equations can be solved by factoring.

### How do you divide a polynomial by a polynomial?

To divide polynomials using long division, first divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient. Multiply the new term by the divisor, and subtract this product from the dividend. This difference is the new dividend.

#### How do you find the quotient of the remainder theorem?

When we divide A by B in long division, Q is the quotient and R is the remainder.

**How do you explain long division method?**

**Why does polynomial long division work?**

It works the same way as euclidean division works for integers: you divide the highest (group of) figure(s) of the dividend by the highest figure of the divisor. Yet in the end you get the quotient and the remainder. You are involving the other terms, in the subtraction steps.