Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to whole number powers and coefficients. For example, 2x² + 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 expression. For example, in the polynomial 4x³ + 2x² - x + 7, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x³ is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms. For example, x² + 2x + 1 is a trinomial.

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How do you add polynomials?

Back

To add polynomials, combine like terms. For example, (2x² + 3x) + (4x² + 5) = 6x² + 3x + 5.

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How do you subtract polynomials?

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To subtract polynomials, distribute the negative sign and then combine like terms. For example, (3x² + 2x) - (x² + 4) = 2x² + 2x - 4.

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What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x² and 5x² are like terms.

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. For example, 4x³ + 2x² - x + 5 is in standard form.

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What is the difference between a polynomial and a non-polynomial?

Back

A polynomial consists of terms with non-negative integer exponents, while a non-polynomial may have negative exponents, fractional exponents, or variables in the denominator. For example, 1/x is a non-polynomial.