Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees.

Front

What is the degree of a polynomial?

Back

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

Front

Classify the polynomial 4x^3 + 2x^2 - x + 5 by its degree.

Back

Cubic (degree 3) because the highest exponent is 3.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c).

Front

What is the divisor in synthetic division when dividing by (x - 2)?

Back

The divisor is 2.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients.

Front

What is a zero of a polynomial?

Back

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

Front

What does it mean for a zero to have a multiplicity of 2?

Back

A zero has a multiplicity of 2 if it is a root of the polynomial that appears twice, indicating that the graph touches the x-axis at that point.

Front

What is a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b.