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Polynomials 1 2 3 Monomials & Operations
Polynomial Degrees & Operations 3 Practice Problems
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Monomials
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Definitions Monomial Number Variable
Product of a number and a variable Can not contain Variables in the exponent Variables with negative exponents Variables under radicals
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Definitions Constants Coefficient Degree of a monomial
Monomials that contain no variables Real numbers Coefficient Constant multiplied to a variable 2 is the coefficient in 2x Degree of a monomial Sum of the exponents of a monomial 12g7h4 is 7+4=11
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Definitions Power Simplify an expression Exponent x2
Rewrite without parenthesis or exponents
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Exponent Rules Rule Examples
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Powers Rules Rule Example
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Examples Simplify
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Examples Simplify
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Examples Simplify:
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Examples Simplify:
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Examples Simplify
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Polynomials
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Definitions Polynomial Terms Trinomial Binomial Monomial
Sum of monomials Terms Monomials that make up the polynomial Like Terms are terms that can be combined Trinomial Has 3 unlike terms Binomial Has 2 unlike terms
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Degree of Polynomials Defined by the highest degree term
Example: Determine if is a polynomial and if so, what degree. Both terms are monomials, so it is a polynomial. The highest term is 8 (3+5), making it an 8th degree polynomial
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Another Example Determine if is a polynomial and if so, what degree.
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Subtraction Distribute the -1 Group like terms Combine like terms
Example:
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Basic Multiplication Distributive property applies Example:
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Multiply Polynomials Steps
Multiply the first term of the first polynomial to EACH term of the second polynomial (Distributive Property) Repeat for EACH term in the first polynomial Combine like terms
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Binomial Example
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Binomial/Trinomial Example
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Practice Problems
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