Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c), which allows for quicker calculations compared to long division.

Front

What is the first step in synthetic division?

Back

The first step is to set up the synthetic division by writing down the coefficients of the polynomial and the value of c from the divisor (x - c).

Front

How do you bring down a number in synthetic division?

Back

To bring down a number in synthetic division, you simply write the first coefficient directly below the line.

Front

What do you do after bringing down the first coefficient in synthetic division?

Back

After bringing down the first coefficient, you multiply it by the value of c and write the result under the next coefficient.

Front

What is the purpose of multiplying coefficients in synthetic division?

Back

Multiplying coefficients helps to combine terms and progressively build the quotient of the polynomial division.

Front

How do you add numbers in synthetic division?

Back

You add the number you just wrote under the next coefficient to that coefficient itself to get the new coefficient.

Front

What is the final result of synthetic division?

Back

The final result of synthetic division is the quotient polynomial and a remainder, if any, represented as a constant.

Front

How do you express the answer from synthetic division?

Back

The answer is expressed as the quotient polynomial followed by the remainder over the divisor.

Front

What is the significance of the remainder in synthetic division?

Back

The remainder indicates how much is left over after the division; if it is zero, the divisor is a factor of the polynomial.

Front

What is the relationship between synthetic division and polynomial roots?

Back

If the remainder is zero when using synthetic division, it indicates that the value c is a root of the polynomial.