Polynomial Long and Synthetic Division

Front

What is Polynomial Long Division?

Back

A method for dividing a polynomial by another polynomial of the same or lower degree, similar to long division with numbers.

Front

What is Synthetic Division?

Back

A simplified form of polynomial division that is used when dividing by a linear factor, making calculations easier and faster.

Front

What is the first step in Synthetic Division?

Back

Bring down the first coefficient of the polynomial.

Front

How do you set up Synthetic Division?

Back

Write the coefficients of the polynomial in a row and place the zero of the divisor to the left.

Front

What does the remainder represent in Polynomial Division?

Back

The remainder is what is left over after dividing the polynomial, indicating that the divisor does not evenly divide the polynomial.

Front

What is the significance of the degree of a polynomial in division?

Back

The degree determines the highest power of the variable in the polynomial and affects the number of zeros needed in Synthetic Division.

Front

How do you check the correctness of Polynomial Division?

Back

Multiply the quotient by the divisor and add the remainder; the result should equal the original polynomial.

Front

What happens if the remainder is zero in Polynomial Division?

Back

It means that the divisor is a factor of the polynomial.

Front

What is the role of coefficients in Synthetic Division?

Back

Coefficients are the numerical factors in front of the variable terms and are used in the calculations during Synthetic Division.

Front

What is the process of 'dropping down' in Synthetic Division?

Back

It refers to bringing down the next coefficient after performing a multiplication and addition step.