Adding Polynomials

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 4x^3 - 5x^2 + 3x is a polynomial.

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What does it mean to add polynomials?

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Adding polynomials involves combining like terms from two or more polynomial expressions to form a new polynomial.

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What are like terms in polynomials?

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Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and -5x^2 are like terms.

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How do you combine like terms?

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To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 4x = 7x.

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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 -3.

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What is a binomial?

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A binomial is a polynomial with exactly two terms, such as 3x + 4.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms, such as x^2 + 2x + 1.

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How do you classify polynomials by the number of terms?

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Polynomials can be classified as monomial (1 term), binomial (2 terms), trinomial (3 terms), or polynomial (more than 3 terms).

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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 expression. For example, in 4x^3 - 5x^2 + 3x, 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 4x^3 - 5x^2 + 3x, the leading coefficient is 4.