College Algebra I am going to go through the lesson prior to answering questions regarding 01 Homework Hopefully this will pre empt some questions Timely analysis your own work personally I learn from my errors Verbalize situations What did I do wrong Why was is wrong What did I need to do right Why is this way right Keep this in mind as you take notes Natural Counting Integers Rational Irrational 1 3 3 5 5 2 Given ax2 bx c Usual thought x variable a b c constants 2 Textbooks and some teachers lull us into complacency regarding equations and format Linear equations is a good example of this I hope to encourage your perceptions out of this mathematical rut of how things are represented or mentally translated Most books teach the following Slope Intercept Form y mx b Ax By C Standard Form y y1 m x x1 Point Slope Form c pn d pn c d Profit price quanity cost 3 What if we are talking about a Building B Ladder L Ground Distance G L B G Used to represent and unknown quantity or a changing value x 3x 2y y 2 mx b 0 Parts Coefficient Variable Monomials Polynomial multiple terms 0 1 Remember you may have definitions 4 12 To add or subtract one must have like terms 3xy 4xy 7xy 3xy 4x is in simplified form 5 3 6 4 7 Multiply like Add exponents Bases am an am n 32 34 32 4 36 3 3 4 Exp raised to an Exp Multiply exponents am n am n 32 4 32 4 38 5 3 8 9 7 4 Divide like Bases Subtract exponents am an am n 34 32 34 2 32 3 4 3 Qty raised to an Exp Distribute exponents ab m ambm 3x 4 34x4 3 3 Number raised to a neg Exp a m 3 2 4 the reciprocal 1 am 1 32 1 9 6 8 0 1 Degrees will be dependent on the definition of the variables The degree is the highest combined value of the exponents of one term Degree of x2y 3 Degree of xy 2 Therefore the degree of 3x2y 4xy 3 8 0 1 Generally speaking the degree of 3x2y 4xy 3 How will this change is y is defined as a constant and x is a variable 8 0 1 Generally speaking the degree of 3x2y 4xy 3 How will this change is y is defined as a constant and x is a variable The Degree 2 because 2 is the highest exponent of the VARIABLE 7 3 3 What is the degree of f x f x x6 3x5 3x4 2x3 2x2 x 3 What is the degree 11x4y 3x3y2 7x2y3 6xy4 What is the degree if y is a variable g x 11x4y 3x3y2 7x2y3 2xy4 3 72 2 3 f x x6 3x5 3x4 2x3 2x2 x 3 g x 11x4 3x3 7x2 2x 1 f x g x 2 f x g x 3 f g x 3 72 2 3 f x x6 3x5 3x4 2x3 2x2 x 3 g x 11x4 3x3 7x2 2x 1 f x g x x6 3x5 3x4 2x3 2x2 x 3 11x4 3x3 7x2 2x 6 5 x 3x 14x4 5x3 5x2 3x 3 Possible questions What is the degree What is the coefficient of the x cubed term 8 3 72 2 3 f x x6 3x5 3x4 2x3 2x2 x 3 g x 11x4 3x3 7x2 2x 2 f x g x distributive property This could be ugly if one was asked to complete the multiplication x6 3x5 3x4 2x3 2x2 x 3 11x4 3x3 7x2 2x 11x10 3x9 7x8 2x7 33x9 9x8 21x7 6x6 33x8 9x7 21x6 6x5 what is the degree of the product 3 72 2 3 f x x6 3x5 3x4 2x3 2x2 x 3 g x 11x4 3x3 7x2 2x 3 f g x 11x4 3x3 7x2 2x 6 3 11x4 3x3 7x2 2x 5 3 11x4 3x3 7x2 2x 4 2 11x4 3x3 7x2 2x 32 11x4 3x3 7x2 2x 2 11x4 3x3 7x2 2x 3 11x4 3x3 7x2 2x 6 116x24 36x18 76x12 64x6 what is the degree 2 9 add subtract multiply divide quantities exponents Be SPECIFIC Be SPECIFIC 9 2 9 3x2y 4xy 3 x 2 y 4 x y 4Ab 5aB3 4 A b 5 a B 3 Case Sensitive 7 x2 Quantities y 2z 7 x 2 2 z y No extra spaces 5 9 http math exeter edu rparris 10