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Roly Poly. Divide and Conquer!. Get to the root of the Problem!. 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. - PowerPoint PPT Presentation
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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