## What is the quotient when using synthetic division?

P(x) = Q(x)· D(x) + R(x). P(x) is the dividend, Q(x) is the quotient, and R(x) is the remainder.

## How do you write the remainder in synthetic division?

1 Answer. Elizabeth P. The remainder in synthetic division could be written as a fraction or with R written in front of it. If writing as a fraction, the remainder is in the numerator of the fraction and the divisor is in the denominator.

What is an example of synthetic division?

Example: Using Synthetic Division to Divide a Third-Degree Polynomial. Use synthetic division to divide 4×3+10×2−6x−20 4 x 3 + 10 x 2 − 6 x − 20 by x+2 . The binomial divisor is x+2 x + 2 , so k=−2 k = − 2 . Add each column, multiply the result by –2, and repeat until the last column is reached.

### What is quotient and remainder example?

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. Here the remainder is greater than the quotient.

### 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.

How do you find the quotient and remainder of a polynomial?

The quotient and remainder can then be determined as follows:

1. Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of x, which in this case is x).
2. Multiply the divisor by the result just obtained (the first term of the eventual quotient).

#### How do you do synthetic division step by step?

Synthetic division is another way to divide a polynomial by the binomial x – c , where c is a constant.

1. Step 1: Set up the synthetic division.
2. Step 2: Bring down the leading coefficient to the bottom row.
3. Step 3: Multiply c by the value just written on the bottom row.
4. Step 4: Add the column created in step 3.

#### What is quotient remainder dividend divisor?

So, the number which is getting divided here is called the dividend. The number which divides a given number is the divisor. And the number which we get as a result is known as the quotient. The divisor which does not divide a number completely produces a number, which is referred to as remainder.

What is the remainder when the polynomial 6x 2 11x 3?

The remainder when the polynomial 6×2 + 11x – 3 is divided by 2x – 1 is 4.

## Which polynomial is the quotient?

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).

## What is the remainder of 74 divided by 7?

Extra calculations for you Using a calculator, if you typed in 74 divided by 7, you’d get 10.5714. You could also express 74/7 as a mixed fraction: 10 4/7.

What does quotient and remainder mean?

When you compute the quotient in division, you may end up with a remainder. The result of division is called the quotient. The number left over is called the remainder. The remainder is part of the result. Here is a quotient example with a remainder:

### Can the 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. Here the remainder is greater than the quotient.

### What is synthetic division and remainder theorem?

The remainder is 3. Our question was: (x 3+2x 2+x+5) ÷ (x+2) The opposite of the constant in our binomial is

• The remainder is 2. Our question was: (x 3 – 6x 2 – 2x+14) ÷ (x – 6) The opposite of the constant in our binomial is
• The remainder is 6.
• The remainder is 4.
• The remainder is 0.
• How do you divide synthetic division?

Set the divisor to zero to find the number to put in the division box.

• Express the dividend in standard form.
• Now,bring down the leading coefficient in the dividend.
• Place the product of the number you brought down and the number in the division box in the preceding column.