Practice 4.7

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.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

How do you find the rational zeros of a polynomial?

Back

To find the rational zeros of a polynomial, use the Rational Root Theorem, which states that any rational solution, expressed as a fraction p/q, has p as a factor of the constant term and q as a factor of the leading coefficient.

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 of a polynomial is the coefficient of the term with the highest degree, and it determines the end behavior of the polynomial's graph.

Front

What does it mean for a polynomial to be in standard form?

Back

A polynomial is in standard form when its terms are arranged in descending order of degree, from highest to lowest.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers, while a rational function is a ratio of two polynomials.

Front

What is the purpose of factoring a polynomial?

Back

Factoring a polynomial simplifies it and can help find its roots or zeros, making it easier to solve equations.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.