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Understanding Monomials, Polynomials, and Their Degrees in Algebra

This lesson covers the fundamental concepts of algebra, including the definition of a monomial as a real number, variable, or product of real numbers and variables. We explore the degrees of monomials and polynomials, including key terms such as constant, linear, quadratic, cubic, quartic, and quintic terms. The standard form of polynomial functions is discussed, along with how to identify binomials and trinomials. Understanding these concepts is essential for mastering algebra and polynomial functions.

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Understanding Monomials, Polynomials, and Their Degrees in Algebra

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  1. Algebra 25-1 (Day 1) • MONOMIAL (p.280) a real number, a variable, or a product of a real number and 1 or more variables • DEGREE OF A MONOMIAL IN ONE VARIABLE (p.280) the exponent of the variable

  2. Algebra 25-1 (Day 1) • POLYNOMIAL (p.280) a monomial or the sum/difference of monomials • BINOMIAL (p.281) the sum/difference of 2 monomials • TRINOMIAL (p.281) the sum/difference of 3 monomials

  3. Algebra 25-1 (Day 1) • DEGREE OF A POLYNOMIAL IN ONE VARIABLE (p.280) the greatest degree of its monomials • POLYNOMIAL FUNCTION OF x (p.280) a polynomial whose only variable is x

  4. Algebra 25-1 (Day 1) • STANDARD FORM OF A POLYNOMIAL FUNCTION (p.281) a polynomial whose terms are arranged in descending degree

  5. Algebra 25-1 (Day 1) • CONSTANT TERM: a term whose degree is 0 (just a number) • LINEAR TERM: a term whose degree is 1

  6. Algebra 25-1 • QUADRATIC TERM: a term whose degree is 2 • CUBIC TERM: a term whose degree is 3

  7. Algebra 25-1 • QUARTIC TERM: a term whose degree is 4 • QUINTIC TERM: a term whose degree is 5

  8. Algebra 25-1

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