Polynomial Characteristics

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, combined using addition, subtraction, and multiplication.

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 3x^2 + 2x + 1, the degree is 2.

Front

How do you determine the leading coefficient of a polynomial?

Back

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

Front

What does the end behavior of a polynomial refer to?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as the input (x) approaches positive or negative infinity.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines the direction of the ends of the graph of the polynomial. If it is positive, the right end goes up; if negative, the right end goes down.

Front

What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero. It is also known as a root or solution of the polynomial.

Front

How many zeros can a polynomial of degree n have?

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A polynomial of degree n can have at most n zeros, counting multiplicities.

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What is the difference between a polynomial and a monomial?

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A polynomial is a sum of one or more monomials, while a monomial is a single term consisting of a coefficient and a variable raised to a non-negative integer power.

Front

What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms, starting with the term of the highest degree.

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What is a factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors, which can be linear or irreducible polynomials.