operation of 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 is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 - 5x^2 + 3x, the degree is 3.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms. For example, 3x + 5 is a binomial.

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What is a monomial?

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A monomial is a polynomial that contains exactly one term. For example, 7x^2 is a monomial.

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How do you add polynomials?

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

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How do you subtract polynomials?

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To subtract polynomials, distribute the negative sign and then combine like terms. For example, (4x^2 + 3x) - (2x^2 + 5) = (4x^2 - 2x^2) + 3x - 5 = 2x^2 + 3x - 5.

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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). For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

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What is a cubic polynomial?

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A cubic polynomial is a polynomial of degree 3. For example, 2x^3 - 4x^2 + x - 5 is a cubic polynomial.

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What is a quartic polynomial?

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A quartic polynomial is a polynomial of degree 4. For example, x^4 - 3x^3 + 2x^2 - x + 1 is a quartic polynomial.

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What are like terms?

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