Math Q2 Week 2

• When translating phrases into algebraic expressions, you need to identify keywords and phrases which specifically refer to a mathematical operation (addition, subtraction, multiplication, and division). Usually, translation is done by simply following the order in which the terms and operations are given.  Exceptions occur for some verbal statements involving subtraction and division.
• Verbal Phrase – a phrase which may involve variables, operators and signs expressed in words

  
  

  
  

  Verbal sentence - a mathematical sentence that is expressed in words
• Algebraic Expression

  •       An expression consisting of one or more numbers and variables along with one or more arithmetic operations

  •       An expression that contains a variable, a constant, or a combination of constants and variables

  Variable

  Any letter in the English alphabet (or symbol) that represents a number

   

  Constant

  •       Symbol that has a fixed value

  •       A specific value

  In the expression an , n is referred to as the exponent of the base a.

  The exponent tells how many times the base is to be used as a factor in multiplying it by itself.
• A polynomial is a special type of algebraic expression that contains a specific number of terms each of which is of the form axn or bxmyn where a and b are real numbers, and m and n are whole numbers.

  A polynomial is an algebraic expression in which the following characteristics occur:

  1.    The variables do not have negative nor fractional exponents.

  2.    The variables do not appear under the radical sign.

  3.    The variables are not in the denominator.
• Numerical Coefficient - the numerical factor in a term

  Literal Coefficient - the literal factor in a term
• If It has one term, therefore this is a monomial

  It has two terms, therefore this is a binomial

  It has three terms, therefore this is a trinomial

  It has more than 3 terms, therefore this is a multinomial

   
• • Degrees the highest exponent (if there is only 1 variable) or the highest sum of exponents of the variables in a term
• Constant – a polynomial of degree zero

  Linear – a polynomial of degree one

  Quadratic – a polynomial of degree two

  Cubic – a polynomial of degree three

  Quartic – a polynomial of degree four

  Quintic – a polynomial of degree five

  * The next degrees have no universal names yet so they are just called “polynomial of degree ____.”
• A polynomial is in Standard Form if its terms are arranged from the term with the highest degree, up to the term with the lowest degree.

  If the polynomial is in standard form the first term is called the Leading Term, the numerical coefficient of the leading term is called the Leading Coefficient.
• Mathematical Phrase is a group of mathematical symbols which does not express a complete thought.

  Mathematical sentence is a group of mathematical symbols which expresses a complete thought
• An algebraic expression is any combination of numbers and variables using one or more of the fundamental operations of algebra.
• Algebraic expressions can be evaluated when the value of the variables are known.
• In order to evaluate an algebraic expression, substitute the given value in each quantity and perform the indicated operation.