Long and Synthetic Division

Front

What is Long Division in Algebra?

Back

A method for dividing polynomials, similar to long division with numbers, where the dividend is divided by a divisor to find the quotient and remainder.

Front

What is Synthetic Division?

Back

A simplified form of polynomial division that is used when dividing by a linear factor, typically represented as (x - c).

Front

How do you set up Long Division for polynomials?

Back

Write the dividend under the long division symbol and the divisor outside. Align the terms according to their degrees.

Front

What is the first step in Long Division of polynomials?

Back

Divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient.

Front

What do you do after finding the first term in Long Division?

Back

Multiply the entire divisor by the first term of the quotient and subtract this from the dividend.

Front

What is the purpose of bringing down the next term in Long Division?

Back

To create a new polynomial that can be divided again by the divisor.

Front

What is the Remainder Theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

How do you express the result of a polynomial division?

Back

The result is expressed as the quotient plus the remainder divided by the divisor.

Front

What is the significance of the degree of the polynomial in Long Division?

Back

The degree helps determine how many times you can divide and how to align terms during the division process.

Front

What is a common mistake in Long Division of polynomials?

Back

Forgetting to subtract the entire product of the divisor and the quotient term from the dividend.