Polynomial Review

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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. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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What does it mean to simplify a polynomial expression?

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Simplifying a polynomial expression involves combining like terms and reducing the expression to its simplest form, making it easier to work with.

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How do you combine like terms in a polynomial?

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To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

Front

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 expression. For example, in 4x^3 + 2x^2 - x, the degree is 3.

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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^4 + 3x^2 - 2, the leading coefficient is 5.

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

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A monomial is a polynomial with one term, a binomial has two terms, and a trinomial has three terms. For example, 3x (monomial), 2x + 5 (binomial), and x^2 + 3x + 4 (trinomial).

Front

How do you perform polynomial addition?

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To add polynomials, combine like terms from each polynomial. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

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How do you perform polynomial subtraction?

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

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What is the product of two polynomials?

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The product of two polynomials is found by using the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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What is the result of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

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The result is -8n^2 - 8n + 3.