Show:
Are we or are we not?
Terms of the Polynomials
Remainder or
Factors
Write the polynomial
function and its behavior
Rational and Complex Zeros
100
Is P(x) = x^3 – 2x^2 + 3x – 1 a polynomial and what is its degree?
Yes, degree 3
100
What is the leading coefficient of P(x) = -2x^2 + 4x^3 - 2x^5 - 1?
-2
100
What is the remainder if P(x) = 2x^3 - 3x^2 + x - 1 is divided by x - 1?
-1
100
Write the polynomial function in factored form with zeros: x = 1 , x = 2, x = 3.
P(x) = (x - 1) (x - 2) (x - 3)
100
Find a third - degree polynomial with the given zeros: 0, 2, 5
P(x) = x (x - 2)(x - 5)
200
True or False: All graphs of polynomial functions cross the x - axis.
false
200
What is the missing term of P(x) = 2x^4 - 3x^3 + 5x^2 - x ?
constant
200
Is (x - 2) a factor of f(x) = x^3 + 2x^2 -5x - 6
yes, remainder is 0
200
What is the end behavior of the graph of f(x) = - x^4 + 3x^ 3 - x^2 + x - 1 ?
As x increases without bounds, f(x) decreases without bounds; as x decreases without bounds, f(x) decreases without bounds.
200

Find a fourth - degree polynomial with the given zeros: -1, 1, -2, 2

P(x) = x^4 - 5x^2 + 4

300
Yes or No: Using the end behavior of P(x) = x^3 - 2x^2 + 1, the graph falls to the right.
No.
300
What is the leading term of P(x) = -2x^3 + 3x - x^5?
-x^5
300
Find the other zeros if 2 is a zero of f(x) = x^3 + 2x^2 -5x - 6.
-1 and -3
300
Describe the multiplicity and behavior of the graph at its zeros. P(x) = x (x - 1)^3 (x + 2)^2
x = 0 mult 1 - crosses ; x = 1 mult. 3 - forms a terrace/flattens ; x = -2 mult. 2 - touches/tangent
300

A third degree polynomial with roots -2 multiplicity of 3

x^3 + 6x^2 + 12x + 8

400
Is P(x) = πx^3 – 2x^2 + 3x a polynomial?
yes
400
How many possible positive zeros are in P(x) = 2x^4 - 3x^3 + x^2 - x + 2.
4 or 2 or 0
400
Use the IVT to determine if there is a zero between x = 1 and x = 2 on the graph of P(x) = x^4 - 3x^3 + x^2 + 2.
Yes. f(1) = 1 and f(2) = -2
400
How many zeros are there in P(x) = x^5 - 2x^4 + x - 1? List all the possibilities of zeros using Descarte's rule.
5 ; 3 or 1 positive roots, 0 negative root, 2 or 4 imaginary roots
400

What is the degree of the polynomial if it has 2 positive roots, and 3 negative roots

5
500
Is P(x) = x - (1/3)x^2 a polynomial?
yes
500
What are the x - intercepts of f(x) = x (x + 1) (x - 2) (2x - 1)?
0, 1/2 , -1, 2
500
Use synthetic division to find the quotient when f(x) = 2x^3 + 3x^2 -5x -6 is divided by (x + 2).
2x^2 - x - 3
500
Find all the zeros, multiplicities, behavior of the graph at its zero for the polynomial P(x) = 11x (x - 1)^5 (x + 1).
0, multiplicity 1 and crosses 1, multiplicity 5 and it flattens or forms a terrace -1, multiplicity 1 and crosses
500

 sqrt5, -sqrt5 and -1

A third degree polynomial with given roots

x^3 - x^2 - 5x + 5