Polynomial Operations

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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, along with coefficients. For example, 2x^2 + 3x - 5 is a polynomial.

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What are like terms in a polynomial?

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

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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, (2x^2 + 3x) + (4x^2 + 5x) = (2+4)x^2 + (3+5)x = 6x^2 + 8x.

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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 the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

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What is the difference between a monomial and a polynomial?

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A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 3x is a monomial, while 3x + 2 is a polynomial.

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How do you subtract polynomials?

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To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (3x^2 + 4x) - (2x^2 + x) = (3-2)x^2 + (4-1)x = x^2 + 3x.

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of lower degree, similar to numerical long division. It involves dividing the leading terms, multiplying, and subtracting.

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What is the result of multiplying two polynomials?

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The result of multiplying two polynomials is a new polynomial formed by distributing each term in the first polynomial to every term in the second polynomial. For example, (x + 2)(x + 3) = x^2 + 5x + 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 5x^2, 5 is the coefficient.

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What does it mean to simplify a polynomial?

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To simplify a polynomial means to combine like terms and express it in its simplest form. For example, simplifying 3x + 2x - 5 results in 5x - 5.