3.2-3.3: Synthetic Division and Rational Root Theorem

Front

What is Synthetic Division?

Back

A method used to divide a polynomial by a linear factor of the form (x - c) efficiently without using long division.

Front

What is the Rational Root Theorem?

Back

A theorem that provides a list of possible rational roots of a polynomial equation based on the factors of the constant term and the leading coefficient.

Front

How do you determine possible rational roots using the Rational Root Theorem?

Back

List all factors of the constant term and divide them by all factors of the leading coefficient.

Front

What is a zero placeholder in synthetic division?

Back

A zero placeholder is used in synthetic division to represent missing terms in a polynomial, ensuring proper alignment of coefficients.

Front

If a polynomial is divided by (x - c), what value of c is used in synthetic division?

Back

The value c is the root of the polynomial, which is the value that makes the polynomial equal to zero.

Front

What is the remainder in synthetic division?

Back

The remainder is the value left over after dividing a polynomial by a linear factor, indicating whether the factor is a root.

Front

How do you set up synthetic division for the polynomial x^4 + 3x^2 - 4x - 2 divided by (x - 2)?

Back

Write the coefficients of the polynomial in order, including zero for any missing terms, and use 2 as the divisor.

Front

What is the significance of the leading coefficient in the Rational Root Theorem?

Back

The leading coefficient helps determine the possible rational roots by providing the denominator for the potential roots.

Front

What is the result of dividing (3x^3 - 2x^2 - 7x + 6) by (x + 1) using synthetic division?

Back

3x^2 - 5x - 2 + 8/(x + 1).

Front

What does it mean if a polynomial has a remainder of zero after synthetic division?

Back

It means that the divisor is a factor of the polynomial, and the corresponding value is a root.