Polynomial Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does it mean to simplify a polynomial?

Back

Simplifying a polynomial involves combining like terms and reducing the expression to its simplest form, making it easier to work with.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 4x are not.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5x) = (2x^2 + 4x^2) + (3x + 5x) = 6x^2 + 8x.

Front

How do you subtract polynomials?

Back

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

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, 4x^3 + 2x^2 - x + 7 is in standard form.

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

Front

How do you multiply polynomials?

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To multiply polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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What is the result of multiplying (x + 2)(x + 3)?

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The result is x^2 + 5x + 6, obtained by distributing each term.

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What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, such as 3x^2. A polynomial can have multiple terms, such as 2x^2 + 3x - 5.