Problems
Identify the degree and leading coefficient:
2x4-5x+1
Degree: 4
Leading Coefficient: 2
What is the method for using boxes?
Positive Even leading coefficient=?
lim f(x)= infinity lim f(x)= infinity
x -> -infinity x -> infinity
What is a degree?
largest exponent on the variable
Identify the degree and leading coefficient:
-2x4+5x6+3x-2
Degree: 6
Leading Coefficient: 5
What are you factoring in the factor theorem?
You are factoring the both sides of the equation.
Positive Odd Leading Coefficient =?
lim f(x)= -infinity lim f(x)= infinity
x -> -infinity lim -> infinity
What is a leading coefficient?
Number being multiplied by the variable with the largest number.
Adding and Subtracting Polynomials:
(3+ 4m4-m2)+(5m2+m4+3m3)
5m4+3m3+4m2+3
How can you determine if you are using Synthetic Division?
In synthetic division, unlike long division, you are only concerned with the coefficients in the polynomials.
Negative even leading coefficient =?
lim f(x)= -infinity lim f(x)= -infinity
x -> -infinity lim -> infinity
When the second derivative is negative at x=c, then f(c) is maximum.
Multiplying Polynomials:
(x3-2x-8)(-x2+3x-5)
-x5+3x4-3x3+2x2-14+40
What is Polynomial Division?
An algorithm to solve a rational number that represents a polynomial divided by a monomial or another polynomial.
negative odd leading coefficient =?
lim f(x)= infinity lim f(x)= -infinity
x -> -infinity lim -> infinity
How to find local minimum
If the second derivative at x=c is positive, then f(c) is a minimum.
Factor x2+16
Not factorable because its a plus
What is Factor Theorem?
If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0
Can there be 3 changes to a Descartes rule of signs?
Yes
What is end behavior?
Where the graph is heading towards.