Write the Polynomial Function
Zeros
Random Polynomial Math
Descartes Rule of Signs
Name That Tune
100
Given a zero at x=2 (multiplicity 1) and a zero at x=−1(multiplicity 1), write a polynomial of least degree with a LC of 1 that has these zeros.
f(x) = x2-x-2
100
Find all zeros:
f(x)=x3−4x2−x+4
Zeros: 1,4,−1
100
The zeros of a function represent these of a graph. (What are 3 other words for zeros?)
x-intercepts or roots or solutions
100
Use Descartes' Rule of Signs to determine the maximum number of positive real zeros of f(x)=x4−3x3+2x2−5x+4
max: 4
possible: 4 or 2 or 0
100
1969
"All You Need is Love" by the Beatles
200
Write a polynomial of least degree with real coefficients, leading coefficient 3, and zeros at x=0 (multiplicity 2) and x=4
y = 3x3−12x2
200
Find all zeros for
f(x) = 2x3 + 2x2 - 8x - 8
(-2, 0), (-1, 0), and (2, 0)
200
What is the end behavior of y=x2+2x-3x3-6
What is: Left Up, Right Down
200
Use Descartes' Rule of Signs on f(−x) to determine the maximum number of negative real zeros of f(x)=−x5+2x4+x3−4x+1
max: 2
possible: 2 or 0
200
1997
"My All" by Mariah Carey
300
Construct a polynomial function of least degree with zeros at x=1 and x=1/2 and leading coefficient −2. Express with integer coefficients.
f(x) = −4x2+6x-2
300
Use the Remainder Theorem to solve the following:
When y = x3 + kx2 − 4x + 2. is divided by x + 2 the remainder is 26, find k.
k = 6
300
What is the end behavior of y=2x6+7x3-6x+57
What is: Up, Up
300
2001
"Break Ya Neck" by Busta Rhymes
400
Given zeros at x=−3 (multiplicity 1) and complex zero 2+i, write the real-coefficient polynomial of least degree with leading coefficient 1.
f(x) = x3−x2−7x+15
400
Find all of the zeros of:
y = x3 - 4x2 - 15x + 18
(-3, 0), (1, 0), and (6, 0)
400
Find the zeros and their multiplicities of:
(x2-81)(x2+3x-10)(x-9)2
Zero: 9, Multiplicity: 3
Zero: -5 Multiplicity: 1
Zero: 2 Multiplicity: 1
Zero: -9 Multiplicity: 1
400
For f(x)=x6−x5−5x4+5x3+6x2−6x -5, use Descartes' Rule to list all possible counts of positive and negative real zeros.
+, -, imaginary
3, 3, 0
3, 1, 2
1, 3, 2
1, 1, 4
400
2013
"Still Into You" by Paramore
500
Write a possible equation for the graph
- (x+7)(x+2)(x-1)(x-5)
500
Find the zeros of
y = x3 - 3x2 - 6x + 8
(-2, 0), (1, 0), and (4, 0)
500
Write a possible equation given the zeros:
x= 2, -1, 2/3 Write in factored form, no fractions
y=(x-2)(x+1)(3x-2)
500
2012
"Call Me Maybe" by Carly Rae Jepsen