Standard Form, Graph Behavior and Degree of Polynomials
Adding, Subtracting, multiplying Polynomials
Factor And Identities
Graph of polynomials
Division and Theorems
100
15x4+6x6-12x3+5x2-7
name the degree
6th degree
100
(−6x3 − 4x2 − 8) +(x3 − x2 − 9x + 4).
-5x3-5x2-9x-4
100
(5 − 4x3)(5 + 4x3).
What is 25 − 16x6
100
What are the zeros on the graph
What is x= -3, 2, 5,
100
P(4) = 0 therefore 4 is a zero of P
What theorem
What is the factor theorem
200
64x3 -5x5+36x9 -4x4+2x2+ 1
lead coefficient
What is 36
200
(6x2+3x-7) - (4x2-5x+5)
2x2+8x-12
200
Factor
1 − 125n3.
(1-5n) (1+5n+25n2)
200
Give the factorization for the graph
(x+3)(x-2)2(x-5)
200
Use the remainder theorem to evaluate
f(x)=2x3-3x2+4x+13.
at x=3
What is 52
300
64x5 + 3x2+18x7 + 1
Put in standard form
18x7+64x5+3x2+1
300
(m + n)(m2 − 2mn + 2n2)
m3-m2n+2n3
300
Factor
64x3+27y6
(4x+3y2)(16x2-12xy2+9y4)
300
Where is the graph positive?
(- infinity,-3) and (5, infinity)
300
Use long division
x3+5x2-x-5 divided by (x-1)
x2+6x+5
400
−x4 − 4x3 − x2 + 6x
What is the end behavior of the graph
Both ends go to - infinity
400
(2x-5i)(2x+5i)
4x2+25
400
Expand
(x+y)4
x4+4x3y+6x2y2+4xy3+y4
400
Where is the graph increasing?
-1.5 to 2 and
4 to infinity
400
x3+6x2+3x-10 divided by (x+5)
x2+x-2
500
x3− x2 − 20x + 25
What is the end behavior of the graph
-x goes to - infinity
+x goes to + infinity
500
Identify the polynomial of degree 3 with the following roots
-5, and 4-8i
x3-3x2+40x+400
500
Find the complex zeros
x2+3x+6
(-3 +/- i (the square root of 15))/2
500
What is a multiplicity and what does it do?
A factor that is repeated, an even multiplicity bumps the graph, an odd multiplicity goes through the graph.
500
Name the possible rational roots
4x3+8x2-x-2
+/- 1, +/- 2, +/- 1/2, +/- 1/4