Warm Up: Simplify

Evaluating expressions2/20/14

• 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

• Examples2x 3qw -2z5r

(if there is no coefficient, it is just a one)

6a + b + 2x2y

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 + 25x 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, 5y3, ½ ab3c2

– NOT MONOMIALS• A + c, x/z, 5 + 7ad, 1/y3

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

• 5x2

• x3 + 2x2 _ 3x

• 12x63x5 - 2x8 x2

Degree Practice

• 13 - x26x4 + 5x8x

• x6_ x5 + 2x8 _ x2

• -5x + 3x10 - 7x-8x5

• 50x82x13 - 6x23 + x2x15

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 3x2

– We also can not add 3x and 3xy– Make sure you distribute before combining

PracticeSolve 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 valuesx is the variable

Identifying a, b, and c• If there isn’t an x2 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 + 3x2 = y + 5

y + 5x2 = - 7 + 2x

12x2 - 3 + 5x = y – 2x + 3x2

Standard form practice

-9x + 24x2 = y + 8

15 + y - 6x2 = 17 + 2x

6x2 - 6 + 9x = y + 7 – 2x + 3x2

Exponent Rules

Multiplying exponents• When multiplying terms with different

exponents, we ADD the exponents– Must be the same variable– Example: (2x2)(3x) =

Practice• y3 ● y5 ● y9

• 2x4 ● 3x3

• 7y6 ● 2x5

• 9x3y2 ● x5y-6

Dividing exponents• When dividing terms with different exponents,

we SUBTRACT the exponents– Must be the same variable– Example: (6x2)/(3x) =

Practice• x5 /x3

• 12y5 /4y3

• x9w3/x5w2

• 24x7w4/8x2w8

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(6x23y3)2

• The outer exponent also applies to the coefficients– (6x23y3)2

Practice

• (y3)5

• (x6y2)3

• (5x7y8)3

• ((5x24y3)2)2

Practice