Topic 1: Monomials
Definitions:
Monomial - expression that has only 1 term (a number, a variable, or the product of a number and one or more variables)
Constants - monomials with no variable
Coefficient - numerical factor of a monomial
Degree - named by the highest exponent
Power - exponent
Simplifying an Expression - rewrite the expression without parentheses or negative exponents
Helpful Hints:
Video Examples:
Simplifying Expressions Using Exponent Rules
Monomial - expression that has only 1 term (a number, a variable, or the product of a number and one or more variables)
Constants - monomials with no variable
Coefficient - numerical factor of a monomial
Degree - named by the highest exponent
Power - exponent
Simplifying an Expression - rewrite the expression without parentheses or negative exponents
Helpful Hints:
- When dividing expressions - divide coefficients(big numbers), subtract exponents(little numbers)
Video Examples:
Simplifying Expressions Using Exponent Rules
Negative Exponents
Topic 2: Operations on Polynomials and Functions
Definitions:
Polynomial- monomial or a sum of monomials (can have many terms)
Terms - monomials that make up a polynomial
Like Terms - terms that have the same variable and exponent
Binomial - an expression with 2 terms
Trinomial - an expression with 3 terms
Composition of Functions - combining functions, where you perform one of the functions and then the other
Helpful Hints:
Video Examples:
Adding, Subtracting and Multiplying Polynomials
(note there is an error in the answer to #1 on the practice problems)
Polynomial- monomial or a sum of monomials (can have many terms)
Terms - monomials that make up a polynomial
Like Terms - terms that have the same variable and exponent
Binomial - an expression with 2 terms
Trinomial - an expression with 3 terms
Composition of Functions - combining functions, where you perform one of the functions and then the other
Helpful Hints:
- The degree of a polynomial is the degree of the monomial with the greatest degree
- When multiplying expressions - multiply coeffiecients(big numbers), add exponents(little numbers)
- When dividing expressions - divide coefficients(big numbers), subtract exponents(little numbers)
- When adding or subtracting they must be like terms(same variable, same exponent)- add/subtract the coefficient(big numbers), keep the exponents(little numbers)
- To find an inverse function, exchange x for y
Video Examples:
Adding, Subtracting and Multiplying Polynomials
(note there is an error in the answer to #1 on the practice problems)
Raising to a Power
Degree of Polynomial with One Variable
Topic 3: Dividing Polynomials by a Monomial
Helpful Hints:
Dividing Polynomials by a Monomial
- when dividing, divide the coefficient, subtract the exponents
Dividing Polynomials by a Monomial
Topic 4: Roots of Real Numbers
Definitions:
principal root - non-negative root
Helpful Hints:
Video Examples:
Finding the Nth Roots of Real Numbers
principal root - non-negative root
Helpful Hints:
Video Examples:
Finding the Nth Roots of Real Numbers
Topic 5: Rationalizing the Denominator
Definitions:
like radical expressions-2 radical expression with alike indices and radicands
Helpful Hints:
Video Examples:
Rationalizing Radical Denominators
like radical expressions-2 radical expression with alike indices and radicands
Helpful Hints:
- in order to rationalize a denominator you must multiply by the conjugate
Video Examples:
Rationalizing Radical Denominators