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 a linear polynomial?

Back

A linear polynomial is a polynomial of degree 1, which can be expressed in the form ax + b, where a and b are constants and a ≠ 0.

Front

Identify the degree of the polynomial: 4x^3 + 2x^2 - x + 7.

Back

The degree of the polynomial is 3, which is the highest exponent of the variable.

Front

What is the leading coefficient of the polynomial 3x^4 - 5x^3 + 2?

Back

The leading coefficient is 3, which is the coefficient of the term with the highest degree.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines the direction in which the graph of the polynomial will rise or fall as x approaches positive or negative infinity.

Front

What is the end behavior of a polynomial with an even degree and a positive leading coefficient?

Back

The end behavior will rise on both ends; as x approaches positive or negative infinity, the polynomial approaches positive infinity.

Front

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

Back

The end behavior will fall on the right and rise on the left; as x approaches positive infinity, the polynomial approaches negative infinity.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is expressed as a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n ≠ 0 and the terms are arranged in descending order of degree.

Front

What is the degree of the polynomial 2x^5 - 3x^2 + 4x - 1?

Back

The degree of the polynomial is 5, which is the highest exponent of the variable.