Polynomial Division: Long and Synthetic

Front

What is polynomial division?

Back

Polynomial division is the process of dividing a polynomial by another polynomial, similar to long division with numbers.

Front

What are the two main methods of polynomial division?

Back

The two main methods are Long Division and Synthetic Division.

Front

When is long division preferred over synthetic division?

Back

Long division is preferred when dividing by a polynomial of degree greater than 1.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial division that is used when dividing by a linear factor.

Front

What is the first step in long division of polynomials?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

In synthetic division, what do you place in the left-hand box?

Back

You place the zero of the divisor (the value that makes the divisor equal to zero) in the left-hand box.

Front

What do you do with the remainder in polynomial division?

Back

The remainder is expressed as a fraction over the divisor added to the quotient.

Front

How do you check your work in polynomial division?

Back

You can check your work by multiplying the quotient by the divisor and adding the remainder; it should equal the original polynomial.

Front

What is the result of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

The result is 2x^2 - 1x + 3 - 3/(x + 3).

Front

What is the purpose of adding 0x terms in polynomial division?

Back

Adding 0x terms helps maintain the correct degree of the polynomial during division.