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Warm Up Given f(x)= 3x-x and g(x)=5x+2 Evaluate f (2) 4 a) f(2) g (3 x) 5 x 17 b) g(3-x) f (4) g (8) 50 c) f(4)+g(8) f (3) g (1) 42 d) f(3) * g(1) g ( y 2) 5 y 12 e) g(y+2) Use the graph to find the following: f) f(1) g) f(-2) + f(1) h) f(X) = 0 f(1) = -8 f(-2) + f(1) = 2 f(x) = 0, x = -3, 0, 3 Monomial: A number or a product of numbers and variables with whole number exponents. One term. Examples: 4 2 3 4 x , 4a b,12, x y z Polynomial: A sum or difference of monomials. Examples: x 8x 2 x 8x 2x 3 2 3x 2 2 x 3x3 2 x 2 5 x The degree of a polynomial with only one variable is the largest exponent of that variable. 12x2 - 7 + 4x3 + x7 The Degree is 7 (the largest exponent of x) Degree of a Polynomial x 8x 2 2z 9z 12 3t t 2 3 3 The Standard Form for writing a polynomial is to put the terms with the highest degree first. (highest exponent to lowest exponent) Example: Put this in Standard Form: 3x2 - 7 + 4x3 + x6 The highest degree is 6, so that goes first, then 3, 2 and then the constant last: x6 + 4x3 + 3x2 - 7 Are these polynomials in standard form? 2x 6x 2x x 2 4 3 5 x 3x 8 x 17 3 2 Like Terms Like terms are terms that contain the same variables, with corresponding variables having the same power. Example : 3x2+4x+x2-2 The like terms in this expression are: 3x 2 and x 2 Group the like terms 1. 7x2+8x-2y+8-6x 2. 3x-2y+4x2-y 3. 6y+y2-3+2y2-4y3 (3x 7 x) (14 x 2 x x) 2 3 Line up with like terms Add like terms 2 Write in standard form (descending order) 3 2 14 x 4 x 0 x 9 (2x2+3x-4) + (4x2+4x+8) Line up with like terms Add like terms Write in standard form (descending order) 1. (36 x 6 x 11) (6 x 16 x 5) 2 2 3 16 x 30 x 6 x 16 3 2. 2 (5x 12 6 x ) (15 x 3x 2) 3 2 2 5 x 9 x 3x 14 3 2 (1 x 2 ) (3x 2 2 x 5) Distribute the negative Sign Add like terms Write in standard form Example: 2 (y2-8y+10) - (3y2+8y+10) 1.Distribute the negative Sign 2.Add like terms 3.Write in standard form 1. (3x2+3x+3) - (4x2-2x+1) 2. (3a3+7a-1) - (3a2+3a-4) On a scale of 1-10 how do you feel about this lesson? 1 being super easy I could do this in my sleep. 10 being I’m not going to lie, I fell asleep and have NO clue what is going on!!!!!!! Homework: Work sheet 10.1