Name/Degree/Term
Exponent Rules
+-*/Polynomials
Parent Functions and End Behavior
Zeros Multiplicity
100
24
Constant Monomial
100
x2*x3
x5
100
(3x2+11x+4)+(-5x+x2-13)
4x2+6x-9
100
What is the equation for a linear parent function?
f(x)=x
100
An even degree polynomial has _ number of zeros.
Even.
200
-3x+1
Linear Binomial
200
What is the name of the highest exponent in a polynomial?
The degree.
200
(7x3+2x+2k)-(5k2-5k+5k)
7x3-5k2+2k+2x
200
What is the equation for a cubic parent function?
f(x)=x3
200
What is the multiplicity of zero equal to?
The number of times its corresponding linear function occurs.
300
What is a polynomial?
The sum or difference of many monomials.
300
(-2a3b)2*8ab9
32a7b11
300
18w4x9/14w5x5
9x4/7w
300
Find the degree and leading coefficient of f(x)=4.
Degree: 0
Leading Coefficient: 4
300
f(x)=(x+7)2(2x+1)(x-4)3
Zeros: -7,-1/2,4
Multiplicities: 2,1,3
400
-3/2x4
Quartic Monomial
400
(14w12/7w3)-1
1/2w9
400
Subtract (-10ab+7a2-b2) from (8b2+ab-2a2).
5a2-9ab-9b2
400
Determine the end behavior of this function.
As x moves toward positive infinity, f(x)= positive
As x moves toward negative infinity, f(x)= negative
400
f(x)=x4-2x3-8x2
Zeros: 0,4,-2
Multiplicities: 2,1,1
500
1/2x3-2x2+4x+15
Cubic Polynomial
500
What is the negative exponent rule?
a-m=1/am/1/a-m=am
500
Write -k5-1+8k-3k3+1/4k2 in Standard Form.
-k5-3k3+1/4k2+8k1-1k0
500
What is the equation for a polynomial function?
f(x)=anxn+an-1xn-1+an-2xn-2+...+a2x2+a1x+a0
500
A polynomial function has a zero at -6 (multiplicity 2) and 2 (multiplicity 1). Write a polynomial function in standard form that could represent this function.
f(x)=(x+6)2(x-2)