PreCalculus Flashcard Review - Chapter 2 (Sections 2.1 - 2.4)

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation, in the form of a fraction p/q, must have p as a factor of the constant term and q as a factor of the leading coefficient.

Front

How do you find the remainder of a polynomial when divided by a linear factor?

Back

Use the Remainder Theorem, which states that the remainder of the division of a polynomial P(x) by (x - c) is P(c).

Front

What is the degree of a polynomial?

Back

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

Front

How many roots can a polynomial of degree n have?

Back

A polynomial of degree n can have at most n roots.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor of the form (x - c).

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function as x approaches positive or negative infinity.

Front

What are the possible rational zeros of the polynomial f(x) = 2x^3 - 3x^2 + 4?

Back

The possible rational zeros can be found using the Rational Root Theorem, which suggests testing factors of the constant term (4) over factors of the leading coefficient (2). Possible rational zeros are ±1, ±2, ±4, ±1/2.

Front

What is the difference between a root and a zero of a function?

Back

A root of a function is a value of x that makes the function equal to zero. A zero is the x-coordinate of the point where the graph of the function intersects the x-axis.

Front

How do you determine the number of turning points of a polynomial function?

Back

The maximum number of turning points of a polynomial function is one less than its degree.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.