Each of Exercises 5–8 shows a complex rational expression and the first step taken to simplify that expression. Indicate for each which method is being used: (a) using division to simplify (Method 1) or (b) multiplying by the LCD (Method 2)
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Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
- In Unit 1 you have learnt about the remainder theorem and long division. Compare and contrast the usefulness of both. If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23 x + 2 , make at least three definitive statements about the ???????? and the ??????? that is involved. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x 2 − 4 x – 2are the same in every respect. Provide evidence to support your position. Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic functions may or may not have x-intercepts. Provide evidence to support your position Identify a function 2. Use function notation 3. Use the remainder and factor theorem 4. Identify special characteristics of the linear, quadratic and cubic function graphs.arrow_forwardProve in detail that if A has infimum 2 then B={x∈R|∃a∈A, x=3a} has infimum 6.arrow_forwardThe polynomial of degree 5, P(x)P(x), has leading coefficient 1, has roots of multiplicity 2 at x=5x=5 and x=0x=0, and a root of multiplicity 1 at x=−3x=-3.arrow_forward
- The polynomial of degree 5, P ( x ) , has leading coefficient 1, has roots of multiplicity 2 at x = 1 and x = 0 , and a root of multiplicity 1 at x = − 5 .arrow_forward3. Use division of t therem to solve the problemarrow_forwardThe average pollen count in a certain city on day x of the pollen season is P(x)=8x − 0.2x2 (for 0 < x < 40). On which day is the pollen count highest?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage