Polynomial Functions

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What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n ≠ 0.

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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. For example, 2x^3 + 3x^2 - x + 5.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^5 + 3x^2 - 2, the degree is 5.

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How do you determine the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in the polynomial. For example, in 3x^4 + 2x^3 - x + 7, the leading coefficient is 3.

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What is the maximum number of turns a polynomial graph can have?

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The maximum number of turns a polynomial graph can have is one less than its degree. For example, a polynomial of degree 3 can have a maximum of 2 turns.

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What is the difference between even and odd degree polynomials?

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Even degree polynomials have the same end behavior (both ends go up or both go down), while odd degree polynomials have opposite end behavior (one end goes up and the other goes down).

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How do you add polynomials?

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To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = 7x^2 + 2x + 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, (5x^3 + 2x) - (3x^3 + 4) = 2x^3 + 2x + 4.

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What is a monomial?

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A monomial is a polynomial with only one term, such as 5x^2 or -3xy.

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What is a binomial?

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A binomial is a polynomial with two terms, such as 3x + 4 or x^2 - 5.