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Dr. Claude S. Moore Danville Community College

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Presentation transcript:

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Roly Poly Divide and Conquer! Get to the root of the Problem! Picture this!Pot Pourri

Give the chart of end behavior

Pos/Odd Left down Right up Pos/Even Left up Right up Neg/Odd Left up Right down Neg/Even Left down Right down

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

Describe 3 attributes of a graph given its degree

-Number of roots -Number of turns -End behavior

Tell why an odd degree polynomial has at least one real root.

An odd degree polynomial will have end behavior up and down, so one part of the graph will cross the x-axis

Give the minimum number of real root of an: -odd degree function -even degree function

Odd degree – at least one Even degree- possible none

by (x – 6) Divide:

217 x-6 2x²+6x+37+

Use synthetic division to find P(-2) if P(x) =

-55

Find the remainder if

-3

How many times is x = -1 a root of

3

You know that (x+1) is a factor of the polynomial Find k

k=-4

Find all solutions of : x³ - 3x² - 6x + 8 = 0

x= 1, 4, -2

Find all roots of: x  - 1 = 0

x= 1, -1, i, -i

Find all roots of: x  - 5x² +4 = 0

x = 2, -2, 1, -1

List possible rational roots of: f(x) = x³ + 2x² - 11x - 12

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

If -4 is a root of f(x) = x³ + 2x² - 11x – 12, then find the other roots

x = 3, -1

Graph: f(x) = x³ - 8x² - 4x + 32

Graph: x³ + 5x² - 9x - 45

Graph: f(x) =2x² + 4x - 7

y = 2(x + 1)² -9

Graph: f(x) = x (x + 3)²

Graph: f(x) =

Use synthetic division to divide: (x² +10)  (x+4)

x – 4 + (26/x+4)

Use long division: (3x² + 11x + 1)  (x-3)

3x (61/x-3)

Give an upper bound and lower bound for:

Upper bound: x = 5 Lower bound: x = -1

Write the polynomial in standard form whose roots are 2, 3i, -3i

x³ -2x² + 9x -18

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