Vocab
Parts of a graph
Cubes
Squared
3 and 4 terms
100
Standard Form
Writing a polynomial in descending powers
100
Looking at this graph, what can we tell about the power and coefficent
negative coefficient
odd power
100
Factor (dont solve)
x3−8
(x−2)(x2+2x+4)
100
factor
x2−16
(x+4)(x-4)
100
x2+7x+10
(x+5) (x+2)
x=-5 and -2
200
Degree of a polynomial
The highest exponent in a polynomial
200
tell me the 0's multiplicities and effect
f(x)=(x−4)(x+2)2
4 multiplicity of 1 crosses x axis
-2 multiplicity of 2 bounces off x axis
200
Factor (dont solve)
x3+27
(x+3)(x2−3x+9)
200
factor and solve
x2+36
NOT FACTORABLE
(-6)1/2 and -(-6)1/2
200
2x2+7x+3
(2x+1)(x+3)
x=-1/2 and -3
300
What is the formula for the sum of cubes, the difference of cubes, and the difference of squares?
(a3+b3)=(a+b)(a2-ab+b2)
(a3-b3)=(a-b)(a2+ab+b2)
(a2+b2)=(a+b)(a-b)
300
Find the relative maxima and relative minima of
f(x)=x3−6x2+9x+1
(1,5) -max
(3,1) min
300
Factor and solve
8x3−125
Factored
(2x−5)(4x2+10x+25)
Solves
x= 5/2 and -10(+/-) (-300)1/2/ 8
300
factor and solve
4x4−25
I don't feel like typing out the answer takes too long
300
x4−5x2+6
(x2-2)(x2-3)
pos and neg square root of 3 and 2
400
What are the 4 names we can use to differentiate polynomials by terms and the number of terms
1 term monomial
2 terms binomial
3 terms trinomial
4 terms polynomial
400
what is the domain and range of
g(x)=x4−2x3−3x2+8
domain (-inf, inf)
range (-4.4, inf) (because there is an extrema its not (-inf, inf)
400
Factor and solve
27x3+64=0
(3x+4)(9x2−12x+16)
x=-4/3 and x=12(+/-) (-432)1/2/ 18
400
factor and solve
3x2−75
3(x-5)(x+5)
x= 5 and -5
400
x3−5x2+2x−10
(x-5)(x2+2)
500
what are the 6 ways we can name something by degree
0- constant
1-linear
2-quadratic
3-cubic
4-quartic
5-quintic
500
what is the interval of increasing and decreasing on
f(x)=x3−6x2+9x+1
increasing : (-inf,1) and (3,inf)
decreasing: (1,3)
500
Factor and solve
2x3−54=0
2(x−3)(x2+3x+9)=0
x=3 and x=-3(+/-) (-27)1/2/ 2
500
factor and solve
9x2-36
typing out takes to long :/
500
6x3−9x2+4x−6
(2x-3)(3x2+2)