Dividing Polynomials

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear divisor of the form (x - c) efficiently.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial in descending order.

Front

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

Back

The value of 'c' from the divisor (x - c) used in the division.

Front

How do you find the remainder in synthetic division?

Back

The remainder is the last number obtained after performing synthetic division.

Front

What is the result of dividing 2x^3 - 5x^2 + 3x + 7 by x - 2?

Back

2x^2 - x + 1 + 9/(x - 2)

Front

What is the area of a rectangular pool table represented by the polynomial x^2 + 14x + 40?

Back

The area can be factored to find the dimensions of the table.

Front

If the length of a rectangle is x + 4 and the area is x^2 + 14x + 40, how do you find the width?

Back

Divide the area by the length: width = (x^2 + 14x + 40) / (x + 4).

Front

What is the purpose of adding zeros in synthetic division?

Back

To account for missing degrees in the polynomial when setting up the division.

Front

How many zeros are needed for the polynomial x^6 + 4x^3 + 2 in synthetic division?

Back

4 zeros are needed for the missing x^5, x^4, x^2, and x^1 terms.

Front

When should you use synthetic division instead of long division?

Back

Use synthetic division when dividing by a linear polynomial of the form (x - c) for efficiency.