Synthetic Division

Front

What is synthetic division?

Back

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

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial and the zero of the divisor (c) on the left.

Front

How do you find the zero of the divisor in synthetic division?

Back

If the divisor is (x - c), the zero is c.

Front

What do you do if a term is missing in the polynomial during synthetic division?

Back

You must use a zero as a coefficient placeholder for that missing term.

Front

In synthetic division, what does the left-hand box represent?

Back

The zero of the divisor, which is used to perform the division.

Front

What is the remainder in synthetic division?

Back

The last number obtained after performing synthetic division, representing the leftover part of the polynomial.

Front

How do you handle the coefficients during synthetic division?

Back

You bring down the first coefficient and then multiply and add in a systematic manner.

Front

What is the result of dividing (2x^3 + 3x^2 - 5) by (x - 1) using synthetic division?

Back

2x^2 + 5x + 0 with a remainder of -5.

Front

What is the significance of the remainder in synthetic division?

Back

It indicates whether the divisor is a factor of the polynomial; if the remainder is zero, it is a factor.

Front

What is the formula for synthetic division?

Back

If dividing by (x - c), the formula is: Coefficients of the polynomial, c, and the synthetic division process.