Warm Up: Simplify

Evaluating expressions 2/20/14 Objectives: – Understand and identify the terms associated with expressions – Determine the degree of an expression – Find standard form of an expression – Understand basic exponent rules

Vocab Variable Coefficient Constant Term Monomial Binomial Trinomial Polynomial Degree Quadratic

Variable A variable is a symbol for a number that is not known yet – We usually see variables as letters The most common variable are x and y but a variable can be any letter

Coefficient A coefficient is a big term for a number that is placed before and multiplying the variable in an algebraic expression Examples 2x 3qw -2z5r (if there is no coefficient, it is just a one) 6a + b + 2x 2 y

Constant A constant is a number that does not change – It can be added or subtracted to a variable Any number that is all by itself (it never changes) Example: 5x + 2 5x changes based on x, but the 2 never changes

Term Terms are the parts of the algebraic expression separated by addition and subtraction – Always remember to simplify before deciding how many terms (distribute, add, subtract, etc.) 3x + 2y – 5z 5(2x + 3) = 3x + 2x =

Monomial A monomial is an expression with only one term – This means there is no addition or subtraction A number can be a monomial A variable can be a monomial A monomial can be the product of a number and a variable – MONOMIALS 12, x, 9a, 5y 3, ½ ab 3 c 2 – NOT MONOMIALS A + c, x/z, 5 + 7ad, 1/y 3

Other expressions Monomial = 1 term – 3x4y2z Binomial = 2 terms – 2x + 5 Trinomial = 3 terms – 3z – 2wr + 3z Polynomial = anything with more than 3 terms – Y + 27 – 3x + 8t

Degree of a polynomial The degree of a polynomial is the highest degree of all the terms in the polynomial – Each term has its own degree Add the exponents of the term to find its degree 5x 2 x 3 + 2x 2 _ 3x 12x 6 3x 5 - 2x 8 x 2

Degree Practice 13 - x 2 6x 4 + 5x 8 x x 6_ x 5 + 2x 8 _ x 2 -5x + 3x x -8 x 5 50x 8 2x x 23 + x 2 x 15

Combining like terms We can only add and subtract terms of the same variable and the same exponent – For example we can add 3x and 2x – We can NOT add 3x and 3x 2 – We also can not add 3x and 3xy – Make sure you distribute before combining

Practice Solve for the missing variable in each of the following expressions:

Quadratic equation A quadratic equation is a polynomial with a degree of 2 – Aka “equation of degree 2”

Standard form Standard form of a quadratic equation looks like this: Notice how the exponents on the variable go down by one each time? a, b, and c are known values x is the variable

Identifying a, b, and c If there isn’t an x 2 then the polynomial is not a quadratic – This means that a can never be 0 If there isn’t an x, then we can assume b = 0 – This means that the formula has a 0x If there is no c, then we can assume it is zero

Example Put the following in standard form -x + 3x 2 = y + 5 y + 5x 2 = x 12x x = y – 2x + 3x 2

Standard form practice -9x + 24x 2 = y y - 6x 2 = x 6x x = y + 7 – 2x + 3x 2

Exponent Rules

Multiplying exponents When multiplying terms with different exponents, we ADD the exponents – Must be the same variable – Example: (2x 2 )(3x) =

Practice y 3 ● y 5 ● y 9 2x 4 ● 3x 3 7y 6 ● 2x 5 9x3y 2 ● x 5 y -6

Dividing exponents When dividing terms with different exponents, we SUBTRACT the exponents – Must be the same variable – Example: (6x 2 )/(3x) =

Practice x 5 /x 3 12y 5 /4y 3 x 9 w 3 /x 5 w 2 24x 7 w 4 /8x 2 w 8

Exponent raised to a degree If we have an exponent raised to another exponent – Here we would multiply the exponents If there is more than one variable, they both get the outer exponent(6x 2 3y 3 ) 2 The outer exponent also applies to the coefficients – (6x 2 3y 3 ) 2

Practice (y 3 ) 5 (x 6 y 2 ) 3 (5x 7 y 8 ) 3 ((5x 2 4y 3 ) 2 ) 2

Practice