Behaviors of Polynomials
What parts of the polynomial determine the end behaviors (up or down)?
a) The roots.
b) The factor of the leading coefficient.
c) The sign of the leading coefficient.
d) The degree of the polynomial.
e) The number of terms in the polynomial.
What are c and d?
What is the degree of the polynomial with roots:
-5 and 5i (might be a "trickster")
What is 3rd degree?
5+2i is a zero so _________ also has to be a zero.
What is 5-2i?
There are 5 birds sitting on a fence. You throw a rock at one and hit it. How many are left?
none
If a polynomial function has two local maximums, two local minimums and NO absolute maximums or minimums, which of the following CANNOT be true?
a) The polynomial could have three zeros.
b) The polynomial has no x-intercepts.
c) The ends of the polynomial both point downward.
d) The ends of the polynomial go in opposite directions.
e) The polynomial must have at least one real root.
What are b and c?
The factored form of a polynomial equation with degree 5, leading coefficient -5, and three of the zeros are -5, 5i and
-sqrt5
What is
p(x)=-5(x+5)(x-5i)(x+5i)(x-sqrt5)(x+sqrt5)
Which of the following is a true statement?
a) A quadratic function can have one real and one imaginary zero.
b) A cubic function can have all imaginary zeros.
c) A quadratic function can have all imaginary zeros.
d) A cubic function can have three real zeros and two imaginary zeros.
What is c?
How much dirt is in a hole that is 3 feet deep and has a radius of 5 feet?
No dirt. It's a hole.
If a polynomial has exactly one double root, exactly one triple root and no other roots of any kind, which of the following MUST be true?
a) The ends of the polynomial go in opposite directions.
b) The polynomial has a degree of five.
c) The polynomial has one local maximum and one local minimum.
d) The polynomial could be classified as quadratic or cubic.
e) The polynomial must be a trinomial.
What are a, b and c?
The expanded form of a polynomial equation with degree 3, leading coefficient -2, and two of the zeros are 0 and i
What is
f(x)=-2x^3-2x
State the end behaviors and the number of zeros for:
f(x)= -4x^5+2x^2+2
What is up/down and 5?
Which is heavier, A pound of feathers or a pound of gold?
Neither. They weigh the same
If a polynomial has the following zeros: -5 (multiplicity of 3), 3 and 7 (both with multiplicity of 1) and a negative leading coefficient, which of the following statements must be true?
a) The polynomial has a minimum degree of 5.
b) The polynomial has at least one local max and one local min.
c) The ends of the polynomial are both going downward.
d) The polynomial has at leasts 5 terms.
e) The polynomial passes through the origin.
What are a and b?
Given that 3 is a solution, all of the solutions of
x^3-3x^2+7x-21=0
What are 3,
isqrt7, -isqrt7 ?
Sketch the graph of a fourth degree polynomial with a positive leading coefficient and exactly one real root with a multiplicity of 2. Then put it on the board with a question mark behind it.
? Prof will decide if your graph is correct?
How do crazy people walk through the forest?
they take the psychopath.
Which of the following could NOT be part of the graph of a polynomial function?
a) A break in the curve.
b) A "V" shape.
c) A "U" shape.
d) The line y=x.
e) A vertical line.
f) A circular shape.
What are a, b, e, f
Given that -2 is a zero, the complete factored form of
f(x)=x^3+2x^2+4x+8
What is
f(x)=(x+2i)(x-2i)(x+2)
Given that one of the zeros is i, find all of the zeros of
f(x)=x^4+x^3+2x^2+x+1
What are i, -i and
-1/2+sqrt3/2i, -1/2-sqrt3/2i ?
How many birthdays does the average person have?
One.