3-4 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

Write down the coefficients of the polynomial and the value of c from the divisor (x - c).

Front

How do you set up synthetic division for (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

Use the coefficients [2, 5, 0, 9] and c = -3.

Front

What is the result of synthetic division for (3x^3 + 5x - 1) ÷ (x + 1)?

Back

3x^2 - 3x + 8 - 9/(x + 1).

Front

What does the term 'bring down' mean in synthetic division?

Back

It refers to the process of bringing down the next coefficient after performing a multiplication and addition.

Front

What is the purpose of multiplying in synthetic division?

Back

To find the product of the divisor's root and the current value in the synthetic division process.

Front

What is the final result of the synthetic division of -2x^2 + 4x + 48 by x + 4?

Back

-2x + 12.

Front

What do you do after multiplying in synthetic division?

Back

Add the result of the multiplication to the next coefficient.

Front

What is the significance of the remainder in synthetic division?

Back

It represents the value left over after division, indicating how well the polynomial is divisible by the linear factor.

Front

How do you interpret the coefficients obtained from synthetic division?

Back

They represent the coefficients of the quotient polynomial.