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, along with coefficients. For example, 4x^3 - 2x + 5 is a polynomial.

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What does it mean to add polynomials?

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Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

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What is the FOIL method?

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The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms.

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How do you subtract polynomials?

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To subtract polynomials, you change the sign of the terms in the polynomial being subtracted and then combine like 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 3x^4 + 2x^2 - 5, the degree is 4.

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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.

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What is the product of two polynomials?

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The product of two polynomials is obtained by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

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What is a binomial?

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A binomial is a polynomial that contains exactly two terms. For example, x + 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 does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which can be polynomials of lower degrees.