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Transcript
Name 9/15/14 NSCHS Alg2/Trig Unit 1 Lesson 6 Aim: How do we solve absolute inequalities and add polynomials? Do Now: Solve for x. |13 – x| = 5 Example Remember: absolute positive answers l 3x – 2 l + 8 = 1 value always gives us Absolute Value Inequalities Solve them the same way you would equations except that when you separate the equation into 2 cases, you must flip the sign on case 2. If the variable starts off less than a value, it becomes an intersection. If the variable is more than a value, it becomes a union. Examples: lxl < a x< a and x>-a Examples: lxl > b x>b or x <-b Example: lxl < 5 x < 5 and x > -5 Example: lxl > 14 x > 14 or x < -14 Example: l 4x – 7 l > 13 Practice l 5z + 2 l < 17 Classwork/Homework#4 P. 16 # 8 – 11, 16 – 20, 25, 2 Quiz Wednesday on: Classify Real Numbers – Rational, Irrational, natural, whole, integer Properties of Real numbers – associative, commutative, distributive, inverse, identity Solve equations and inequalities Solve absolute value equations Translating sentence/phrase into an equation/expression. Monomial and Polynomial A monomial is an algebraic expression that is the product of constants and variables. A polynomial is an algebraic expression that is the sum or difference of monomials. Each monomial within the polynomial is called a term. Degree of a Polynomial Essentially, it’s the highest exponent. Ex: 4x4 – 34x2 + 12x7 Ex: 5 Hint: When you get a long convoluted polynomial, arrange the terms from highest exponent to lowest exponent. Adding Polynomials In order to add polynomials, you can ONLY add like terms together. Terms are considered like terms iff they contain the EXACT same variables risen to the EXACT same exponents. Determine the Sum of: 4x2 + 7x – 4 and 8x2 -12x + 13 Determine the Sum of: 3t2 – 7t3 – 6t + 15 and 7t3 + 5t – 2t4 + 8 Determine the Sum of: and Subtracting Polynomials Recall: 5 – 13 The same must be applied to polynomials. Subtracting Polynomials Ex: Determine the difference of the following: 4x2 – 3 and 5x2 + 10 Determine the difference of: 4x2 + 7x – 4 and 8x2 -12x + 13