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 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 + 2x^2 - x + 7, 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 the polynomial 5x^4 + 3x^2 - 2, the leading coefficient is 5.

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How do you add polynomials?

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To add polynomials, combine like terms. For example, (3y^2 + y^3 - 5) + (4y^2 - 4y + 2y^3 + 8) = (1y^3 + 2y^3) + (3y^2 + 4y^2) + (-4y) + (3) = 3y^3 + 7y^2 - 4y + 3.

Tags

CCSS.HSA.APR.A.1

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What is the process of multiplying polynomials?

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To multiply polynomials, use 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.

Tags

CCSS.HSA.APR.A.1

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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 trinomial?

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A trinomial is a polynomial that contains exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

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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, 4x is a monomial, while 4x + 3 is a polynomial.

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What is the zero polynomial?

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The zero polynomial is the polynomial that has all coefficients equal to zero. It is represented as 0 and has no degree.

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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).