Chapter 5 - Polynomials

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 - 4x^2 + 3x - 5 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^5 - 3x^2 + 2, the degree is 5.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 3x^4 + 2x^3 - x + 5, the leading coefficient is 3.

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 their degrees. For example, 5x^3 + 2x^2 - x + 7 is in standard form.

Front

What is the domain of a polynomial function?

Back

The domain of a polynomial function is always all real numbers, represented as (-∞, +∞).

Front

How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (2x^2 + 3x) + (4x^2 - 2x) = 6x^2 + x.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 4) = 3x^2 - 1.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial, similar to numerical long division. It involves dividing the leading terms, multiplying, and subtracting.

Front

What is the Remainder Theorem?

Back

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