Roly Poly Divide and Conquer! Get to the root of the Problem!

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Presentation transcript:

Roly Poly Divide and Conquer! Get to the root of the Problem! Eleanor M. Savko Roly Poly Divide and Conquer! Get to the root of the Problem! 4/16/2018 Picture this! Pot Pourri 1pt 1 pt 1 pt 1pt 1 pt 2 pt 2 pt 2pt 2pt 2 pt 3 pt 3 pt 3 pt 3 pt 3 pt 4 pt 4 pt 4pt 4 pt 4pt 5pt 5 pt 5 pt 5 pt 5 pt

Give the chart of end behavior Eleanor M. Savko 4/16/2018 Give the chart of end behavior

Pos/Odd Left down Right up Pos/Even Left up Neg/Odd Right down Eleanor M. Savko 4/16/2018 Pos/Odd Left down Right up Pos/Even Left up Neg/Odd Right down Neg/Even

Eleanor M. Savko 4/16/2018 State end behavior, max. number of turns, max. number of zeros, and min. number of real zeros : x³ - 8x² - 4x + 32

Left down, right up 2 turns max 3 zeros min 1 real zero Eleanor M. Savko 4/16/2018 Left down, right up 2 turns max 3 zeros min 1 real zero

Describe 3 attributes of a graph given its degree Eleanor M. Savko 4/16/2018 Describe 3 attributes of a graph given its degree

-Number of roots -Number of turns -End behavior Eleanor M. Savko 4/16/2018 -Number of roots -Number of turns -End behavior

Tell why an odd degree polynomial has at least one real root. Eleanor M. Savko 4/16/2018 Tell why an odd degree polynomial has at least one real root.

Eleanor M. Savko 4/16/2018 An odd degree polynomial will have end behavior up and down, so one part of the graph will cross the x-axis

Eleanor M. Savko 4/16/2018 Give the minimum number of real root of an: -odd degree function -even degree function

Odd degree – at least one Even degree- possible none Eleanor M. Savko 4/16/2018 Odd degree – at least one Even degree- possible none

Eleanor M. Savko 4/16/2018 Divide: by (x – 6)

Eleanor M. Savko 4/16/2018 217 x-6 2x²+6x+37+

Use synthetic division to find P(-2) if P(x) = Eleanor M. Savko 4/16/2018 Use synthetic division to find P(-2) if P(x) =

Eleanor M. Savko 4/16/2018 -55

Eleanor M. Savko 4/16/2018 Find the remainder if

Eleanor M. Savko 4/16/2018 -3

How many times is x = -1 a root of Eleanor M. Savko 4/16/2018 How many times is x = -1 a root of

Eleanor M. Savko 4/16/2018 3

You know that (x+1) is a factor of the polynomial Find k Eleanor M. Savko 4/16/2018 You know that (x+1) is a factor of the polynomial Find k

Eleanor M. Savko 4/16/2018 k=-4

Find all solutions of : x³ - 3x² - 6x + 8 = 0 Eleanor M. Savko 4/16/2018 Find all solutions of : x³ - 3x² - 6x + 8 = 0

Eleanor M. Savko 4/16/2018 x= 1, 4, -2

Eleanor M. Savko 4/16/2018 Find all roots of: x - 1 = 0

Eleanor M. Savko 4/16/2018 x= 1, -1, i, -i

Find all roots of: x - 5x² +4 = 0 Eleanor M. Savko 4/16/2018 Find all roots of: x - 5x² +4 = 0

Eleanor M. Savko 4/16/2018 x = 2, -2, 1, -1

List possible rational roots of: f(x) = x³ + 2x² - 11x - 12 Eleanor M. Savko 4/16/2018 List possible rational roots of: f(x) = x³ + 2x² - 11x - 12

Eleanor M. Savko 4/16/2018 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

Eleanor M. Savko 4/16/2018 If -4 is a root of f(x) = x³ + 2x² - 11x – 12, then find the other roots

Eleanor M. Savko 4/16/2018 x = 3, -1

Eleanor M. Savko 4/16/2018 Graph: f(x) = x³ - 8x² - 4x + 32

Eleanor M. Savko 4/16/2018

Eleanor M. Savko 4/16/2018 Graph: x³ + 5x² - 9x - 45

Eleanor M. Savko 4/16/2018

Eleanor M. Savko 4/16/2018 Graph: f(x) =2x² + 4x - 7

Eleanor M. Savko 4/16/2018 y = 2(x + 1)² -9

Eleanor M. Savko 4/16/2018 Graph: f(x) = x (x + 3)²

Eleanor M. Savko 4/16/2018

Eleanor M. Savko 4/16/2018 Graph: f(x) =

Eleanor M. Savko 4/16/2018

Use synthetic division to divide: (x² +10)  (x+4) Eleanor M. Savko 4/16/2018 Use synthetic division to divide: (x² +10)  (x+4)

Eleanor M. Savko 4/16/2018 x – 4 + (26/x+4)

Use long division: (3x² + 11x + 1)  (x-3) Eleanor M. Savko 4/16/2018 Use long division: (3x² + 11x + 1)  (x-3)

Eleanor M. Savko 4/16/2018 3x + 20 + (61/x-3)

Give an upper bound and lower bound for: Eleanor M. Savko 4/16/2018 Give an upper bound and lower bound for:

Upper bound: x = 5 Lower bound: x = -1 Eleanor M. Savko 4/16/2018 Upper bound: x = 5 Lower bound: x = -1

Write the polynomial in standard form whose roots are 2, 3i, -3i Eleanor M. Savko 4/16/2018 Write the polynomial in standard form whose roots are 2, 3i, -3i

Eleanor M. Savko 4/16/2018 x³ -2x² + 9x -18

Eleanor M. Savko 4/16/2018 Use Descartes’s rule of signs to determine the number of pos. and neg. zeros. f(x) = x³ + 3x² + 25x + 75

0 positive zeros 3 or 1 negative zeros Eleanor M. Savko 4/16/2018 0 positive zeros 3 or 1 negative zeros