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MarcKrishkePtest2

MarcKrishkePtest2 - Math 1540 Test 1 Name 1 Use the given...

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Math 1540 Test 1 3-points each Name: 1.) Use the given polynomial to answer the following questions. 7 6 5 4 3 2 ( ) 3 6 14 3 33 72 108 window: [-5, 5, 1] and [-150, 150,30] P x x x x x x x x = + - - - - + + (a) Find all local and absolute extreme points and label each point. Round your answers to the nearest hundredth. Local minima: (-2.02, -112.09), (2, 0) Local maxima: (-3, 0), (0.69, 137.27) (b) Find the rational zero(s). Hint: all the factors of 108 are between 1-10. List all the integers p that are factors of the constant term, 108 p: ± 1, ± 2, ± 3, ± 4, ± 6, ± 9, ± 12, ± 18, ± 27, ± 54, ± 108 List all the integers q that are factors of the leading coefficient, 1 q: ± 1 Form all possible ratios p q . p q : ± 1, ± 2, ± 3, ± 4, ± 6, ± 9, ± 12, ± 18, ± 27, ± 54, ± 108 Check 2: 1 3 6 14 3 33 72 108 2 2 10 8 12 30 126 108 1 5 4 6 15 63 54 0 - - - - - - - - - - - - Since P(2) = 0 then x – 2 is a factor. Then 6 5 4 3 2 ( ) ( 2)( 5 4 6 15 63 54) P x x x x x x x x = - + + - - - -

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Math 1540 Test 1 3-points each Check –3: 1 5 4 6 15 63 54 3 3 6 6 0 45 54 1 2 2 0 15 18 0 - - - - - - - - - - Since P(–3) = 0 then x +3 is a factor. 5 4 3 ( ) ( 2)( 3)( 2 2 15 18) P x x x x x x x = - + + - - - Check 2: 1 2 2 0 15 18 2 2 8 12 24 18 1 4 6 12 9 0 - - - Thus, (x – 2) 2 is a factor 2 4 3 2 ( ) ( 2) ( 3)( 4 6 12 9) P x x x x x x x = - + + + + + Check –3: 1 4 6 12 9 3 3 3 9 9 1 1 3 3 0 - - - - - Thus, (x + 2) 3 is a factor 2 2 2 ( ) ( 2) ( 3) ( 1)( 3) P x x x x x = - + + + Solve the depressed equation: 3 2 2 2 3 3 0 ( 1) 3( 1) 0 ( 1)( 3) 0 x x x x x x x x + + + = + + + = + + = 2 2 1 0 3 0 1 3 1 3 1 3 3 x or x x or x x or x x or x i or x i + = + = = - = - = - = ± - = - = = - Answer : The rational zeros are –3 (multiplicity 2), –1 and 2 (multiplicity 2).
Math 1540 Test 1 3-points each (c) Find the intervals where the function is increasing and decreasing. Be sure to label your intervals. The function is increasing on the intervals (–∞,–3)

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MarcKrishkePtest2 - Math 1540 Test 1 Name 1 Use the given...

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