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 and coefficients. For example, 4x^3 + 3x^2 - 2x + 1 is a polynomial.

Front

What does it mean to simplify a polynomial expression?

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Simplifying a polynomial expression means combining like terms to reduce the expression to its simplest form.

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.

Front

How do you add polynomials?

Back

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

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

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What is the product of two binomials?

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The product of two binomials can be found using the distributive property or the FOIL method (First, Outside, Inside, Last). For example, (a + b)(c + d) = ac + ad + bc + bd.

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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, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

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What is the zero product property?

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The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if (x - 3)(x + 2) = 0, then x - 3 = 0 or x + 2 = 0.

Front

How do you multiply a polynomial by a monomial?

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To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial. For example, 3x(2x + 4) = 6x^2 + 12x.

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What is the standard form of a polynomial?

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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 + 5 is in standard form.