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 whole number 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 is the standard form of a polynomial?

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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 + 5 is in standard form.

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

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What is a constant term in a polynomial?

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The constant term in a polynomial is the term that does not contain any variables. For example, in the polynomial 2x^3 - 4x + 7, the constant term is 7.

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How do you add polynomials?

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To add polynomials, combine like terms. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + (2x) + (5) = 7x^2 + 2x + 5.

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What is the product of two polynomials?

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The product of two polynomials is found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

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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 + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors. For example, x^2 - 9 can be factored as (x - 3)(x + 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 one or more terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.