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Roly Poly

Divide andConquer!

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 up2 turns

max 3 zerosmin 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 oneEven degree- possible none

by (x – 6)

Divide:

3 22 6 5x x x

217 x-62x²+6x+37+

Use synthetic division to find P(-2) if P(x) = 3 23 5 5 1x x x

-55

Find the remainder if

5 4 2( 2 4 2) ( 1)x x x x

-3

How many times is x = -1 a root of

5 4 3 23 11 12 4 0x x x x x

3

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

Find k

3 3x kx

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) = 4 213 36x x

Use synthetic division to divide:

(x² +10) (x+4)

x – 4 + (26/x+4)

Use long division:

(3x² + 11x + 1) (x-3)

3x + 20 + (61/x-3)

Give an upper bound and lower bound for:

4 34 15x x

Upper bound: x = 5Lower 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 zeros3 or 1 negative zeros