1 College AlgebraI am going to go through the lesson prior to answering questionsregarding 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 2! "2535π3# " Given: ax2+ bx + cUsual thought:x = variablea, b, & c = constants$ % & $ ' ( ) ' * +' 3Textbooks (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 =• Standard Form = • Point Slope Form = y = mx + bAx + By = Cy – y1= m(x - x1) (• c = pn + d• pn + c = d• Profit = price*quanity - cost4 $ #% #, #• What if we are talking about a:• Building = B• Ladder = L• Ground Distance = GLGB-#% .#, +#/• Used to represent and unknown quantity or a changing value.x y + 23x – 2y mx + b0 - • Parts– Coefficient– Variable– Monomials– Polynomial (multiple terms)0$# % 1$Remember you may have definitions51 2 ' • To add or subtract one must have like terms.3xy + 4xy = 7xy3xy+4x is in simplified form! 3$4 5 +"+"6"7• Multiply like Basesam * an32* 34• Add exponentsam+n32+4= 36! 3$4 3$• Exp raised to an Exp(am )n(32)4• Multiply exponentsam*n32*4= 386! 3$4 8"/"9"7• Divide like Basesam an3432• Subtract exponentsam-n34-2= 32! 3$4• Qty raised to an Exp(ab)m(3x)4• Distribute exponentsambm34x4: 3$! 3$4 3$• Number raised to a neg Expa-m3-2• = the reciprocal1am1 132978 • 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 = 2Therefore the degree of 3x2y + 4xy = 3 0$# % 1$8 • Generally speaking, the degree of 3x2y + 4xy = 3 • How will this change is y is defined as a constant and x is a variable?0$# % 1$8 • Generally speaking, the degree of 3x2y + 4xy = 3 • How will this change is y is defined as a constant and x is a variable?• The Degree = 2 because 2 is the highest exponent of the VARIABLE0$# % 1$8; 3$ 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$f(x) = x6-3x5+3x4-2x3-2x2-x+3g(x) = 11x4-3x3+7x2-2x1. f(x)+g(x) 2. f(x)g(x)3. f(g(x)); 3$ <72 2 => 3$f(x) = x6-3x5+3x4-2x3-2x2-x+3g(x) = 11x4-3x3+7x2-2x1. f(x)+g(x) x6-3x5+3x4-2x3 -2x2 -x+3+ 11x4-3x3+7x2 -2xx6-3x5+14x4-5x3+5x2-3x+3Possible questions..What is the degree? What is the coefficient of the x cubed term?9; 3$ <72 2 => 3$f(x) = x6-3x5+3x4-2x3-2x2-x+3g(x) = 11x4-3x3+7x2-2x2. f(x)g(x) -- distributive propertyThis could be ugly if one was asked to complete the multiplication(x6-3x5+3x4-2x3-2x2-x+3)(11x4-3x3+7x2-2x)=11x10-3x9+7x8 -2x7-33x9+9x8-21x7+6x6+33x8-9x7+21x6-6x5… what is the degree of the product?; 3$ <72 2 => 3$f(x) = x6-3x5+3x4-2x3-2x2-x+3g(x) = (11x4-3x3+7x2-2x)3. f(g(x))(11x4-3x3+7x2-2x)6-3(11x4-3x3+7x2-2x)5 +3(11x4-3x3+7x2-2x)4-2(11x4-3x3+7x2-2x)3-2(11x4-3x3+7x2-2x)2-(11x4-3x3+7x2-2x)+3 = (11x4-3x3+7x2-2x)6- …116x24-36x18+76x12-64x6- …what is the degree?2 =' 9$• add• subtract• multiply• divide• quantities• exponents Be SPECIFIC!!!!!• +• -• *• /• ( )• ^ Be SPECIFIC!!!!!102 =' 9$• 3x2y + 4xy3*x^2*y+4*x*y• 4Ab - 5aB34*A*b-5*a*B^3 (Case Sensitive)• Quantities ((7+x^2)/(2*z))*y• No extra spacesyzx272+? 5 9' •
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