Synthetic Division

Front

What is Synthetic Division?

Back

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

Front

What is the first step in Synthetic Division?

Back

Identify the coefficients of the polynomial and the zero of the divisor (x - c).

Front

How do you find the zero of the divisor x + 3?

Back

Set x + 3 = 0, which gives x = -3.

Front

What is the role of the coefficients in Synthetic Division?

Back

They are used to perform the division process, starting with the leading coefficient.

Front

What does the remainder represent in Synthetic Division?

Back

The remainder is the value of the polynomial evaluated at the zero of the divisor.

Front

If you divide 2x^3 + 5x^2 + 9 by x + 3, what is the first term of the quotient?

Back

The first term of the quotient is 2x^2.

Front

What is the result of dividing x^2 - 6x + 8 by x - 2?

Back

The result is x - 4.

Front

What does f(-2) = -27 indicate in Synthetic Division?

Back

It indicates that -27 is the remainder when the polynomial is evaluated at x = -2.

Front

What is the significance of the remainder in polynomial division?

Back

The remainder indicates how much is left over after division; it can also show if the divisor is a factor.

Front

What is the formula for Synthetic Division?

Back

The formula involves writing the coefficients, bringing down the leading coefficient, and performing multiplication and addition.