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, 2x^2 + 3x + 5 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

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How do you simplify a polynomial expression?

Back

To simplify a polynomial expression, combine like terms by adding or subtracting their coefficients. For example, 3x^2 + 2x^2 simplifies to 5x^2.

Front

What is the process of adding polynomials?

Back

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

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What is the process of subtracting polynomials?

Back

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

Front

What is the distributive property in polynomial operations?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a term by each term in a polynomial.

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How do you multiply polynomials?

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To multiply polynomials, use the distributive property or the FOIL method for binomials. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is a binomial?

Back

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

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

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What is the leading coefficient of a polynomial?

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