Polynomials, Degree and Leading Coefficient – Quick Check

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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 + 1 is a polynomial.

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What does it mean to combine like terms in a polynomial?

Back

Combining like terms means to simplify a polynomial by adding or subtracting terms that have the same variable raised to the same power. For example, in 3x^2 + 4x + 2x^2, you can combine 3x^2 and 2x^2 to get 5x^2.

Front

What is 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 is in standard form.

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What is the leading coefficient of a polynomial?

Back

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

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How do you determine the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial when it is in standard form. For example, the degree of 4x^3 + 2x^2 + 1 is 3.

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What is the degree of the polynomial 2x^4 + 3x^3 + x?

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The degree of the polynomial 2x^4 + 3x^3 + x is 4.

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What is the difference between a monomial, binomial, and trinomial?

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A monomial has one term (e.g., 3x), a binomial has two terms (e.g., 3x + 2), and a trinomial has three terms (e.g., 3x^2 + 2x + 1).

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What does it mean to distribute in polynomials?

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Distributing means to multiply each term inside a parenthesis by a term outside the parenthesis. For example, in 2(x + 3), you distribute to get 2x + 6.

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What is a coefficient in a polynomial?

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A coefficient is a numerical factor in a term of a polynomial. For example, in the term 4x^2, 4 is the coefficient.

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What is the constant term in a polynomial?

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The constant term is the term in a polynomial that does not contain any variables. For example, in the polynomial 3x^2 + 2x + 5, the constant term is 5.