Polynomial Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^3 - 5x + 7 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.

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

How do you find the value of a polynomial function at a specific point?

Back

To find the value of a polynomial function f(x) at a specific point x = a, substitute a into the polynomial and simplify. For example, if f(x) = 2x^3 - 5x^2 + 3x + 7, then f(2) = 9.

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. For example, if f(x) = x^2 - 4, then x = 2 and x = -2 are zeros.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used when dividing by a linear factor of the form (x - c). It is faster and requires less writing.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you determine the number of real zeros of a polynomial?

Back

The number of real zeros of a polynomial can be determined using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots (real or complex).

Front

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

Back

A polynomial is a function that can be expressed as a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.