What is a polynomial
State if the following is a polynomial
f(x)= 3x2 - x-5 + 6x4
No
State the zeros
g(x)= (x + 8)(x - 3)(x + 5)
x = -8, 3, and -5
Describe or sketch the end behavior
f(x)= 4x4 + 6x - 1
right up
left up
State the lead term, degree, and constant term
f(x)= 9x4 + 3x2 + 5x
Lead Term: 9x4
Degree: 4
Constant Term: 0
Rewrite in factored form:
f(x) = x2 + 15x + 50
f(x) = (x + 5)(x + 10)
Describe or sketch the end behavior
g(x)= -5x3 + 2x2 - 4
right down
left up
Create a polynomial with the following features:
- Degree is 8
- 5 terms
- Intercepts y axis at y = -2
f(X) = x8 + x7 + x6 + x5 - 2
Multiply the following together
(x + 5)(x - 3)(x + 7)
x3 + 9x2 - x - 105
What is the lead term and end behavior
h(x)= -3(x - 7)6(x + 2)2(x + 1)
Lead term: -3x9
End behavior: Right down, left up
Create a polynomial with zeros:
- x = 7 (multiplicity 9)
- x = -3 (multiplicity 6)
- x = -5 (multiplicity 2)
f(x) = (x - 7)9(x + 3)6(x + 5)2
Find the intercept(s) for the following polynomials
f(x) = (x + 5)(x - 2)
g(x) = x + 5
x = -5
x = 3
Sketch the following polynomial
f(x)= (x + 6)3(x - 2)(x + 5)2
Look to board
Create a polynomial with the following features:
- Even degree
- 2 terms
- Intercepts y axis at y = -7
- As x increases negatively, y increases negatively
- As x increases positively, y increases negatively
h(x)= -4x6 - 7
Rewrite in factored form.
f(x) = x3 + 11x2 + 34x +24
Known factor: (x + 4)
f(x) = (x + 4)(x + 1)(x + 6)
Sketch the following polynomial
f(x) = x2 + 6x + 7
(hint: rewrite in factored form first)
Look to board