General Characteristics of Polynomials

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, f(x) = 2x^3 - 4x + 7 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 polynomial. For example, in the polynomial f(x) = 3x^4 + 2x^2 - 5, the degree is 4.

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How do you determine the leading coefficient of a polynomial?

Back

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in f(x) = 4x^5 + 3x^3 - 2, the leading coefficient is 4.

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What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, if f(x) = x^2 - 4, the zeros are x = 2 and x = -2.

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What is the maximum number of turning points of a polynomial function?

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The maximum number of turning points of a polynomial function is one less than the degree of the polynomial. For example, a polynomial of degree 3 can have a maximum of 2 turning points.

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What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3, which can be expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

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What is a quartic polynomial?

Back

A quartic polynomial is a polynomial of degree 4, which can be expressed in the form f(x) = ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants and a ≠ 0.

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What is a trinomial?

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A trinomial is a polynomial that consists of three terms. For example, f(x) = x^2 + 3x + 2 is a trinomial.

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What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.