Precalculus Practice Flashcard 2.3

Front

What does f(-2) = -27 tell me?

Back

-27 is the remainder when f(x) is divided by (x + 2).

Front

Perform synthetic division on (x² + 4x - 45) by (x + 9). What is the result?

Back

x - 5

Front

What is the correct polynomial form for the expression after division?

Back

2x³ - x² - 25x - 12

Front

Is the binomial x - 9 a factor of 4x² - 33x - 27?

Back

Yes, it is a factor.

Front

How can I determine if a binomial is a factor using synthetic division?

Back

If the remainder is zero, then the binomial is a factor.

Front

What is synthetic division?

Back

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

Front

What is the Remainder Theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What does it mean if a polynomial has a factor?

Back

It means that the polynomial can be divided by that factor without leaving a remainder.

Front

What is the Factor Theorem?

Back

A polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Front

How do you identify the degree of a polynomial?

Back

The degree is the highest power of the variable in the polynomial.