warm up: simplify. evaluating expressions 2/20/14 objectives: – understand and identify the terms...
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Vocab Variable Coefficient Constant Term Monomial Binomial Trinomial Polynomial Degree QuadraticTRANSCRIPT
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Warm Up: Simplify
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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
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Vocab• Variable• Coefficient• Constant• Term• Monomial• Binomial• Trinomial• Polynomial• Degree• Quadratic
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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
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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
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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
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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 =
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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
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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
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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
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Degree Practice
• 13 - x26x4 + 5x8x
• x6_ x5 + 2x8 _ x2
• -5x + 3x10 - 7x-8x5
• 50x82x13 - 6x23 + x2x15
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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
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PracticeSolve for the missing variable in each of the following expressions:
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Quadratic equation• A quadratic equation is a polynomial with a
degree of 2– Aka “equation of degree 2”
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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
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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
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Example• Put the following in standard form
-x + 3x2 = y + 5
y + 5x2 = - 7 + 2x
12x2 - 3 + 5x = y – 2x + 3x2
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Standard form practice
-9x + 24x2 = y + 8
15 + y - 6x2 = 17 + 2x
6x2 - 6 + 9x = y + 7 – 2x + 3x2
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Exponent Rules
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Multiplying exponents• When multiplying terms with different
exponents, we ADD the exponents– Must be the same variable– Example: (2x2)(3x) =
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Practice• y3 ● y5 ● y9
• 2x4 ● 3x3
• 7y6 ● 2x5
• 9x3y2 ● x5y-6
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Dividing exponents• When dividing terms with different exponents,
we SUBTRACT the exponents– Must be the same variable– Example: (6x2)/(3x) =
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Practice• x5 /x3
• 12y5 /4y3
• x9w3/x5w2
• 24x7w4/8x2w8
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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
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Practice
• (y3)5
• (x6y2)3
• (5x7y8)3
• ((5x24y3)2)2
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Practice