Poly-Properties
What degree is the polynomial
y=3x3 + 2x - 4 + 5x4
4th Degree
Factor the following polynomial.
y = x2 + 5x + 6
y = (x + 3) (x + 2)
Give another word for the 'zero' of a Polynomial.
Root, Solution, or X-Intercept
If you divide a polynomial by a binomial and the remainder is zero, then what does that mean about the binomial compared to the polynomial?
The binomial is a factor of the polynomial.
What letter is used to represent a Complex Number.
i
Give the quadratic equation which has the vertex (-1, 4) and a zero at (1, 0).
y = -(x + 1)2 + 4
What is the degree of the polynomial below?
y = 3x4(4x + 5)2(x - 6)(x + 2)5
12th degree
Give the zeros of the polynomial below
y = x(x - 4)(2x + 5)
x = 0, 4, -5/2
Synthetic Division only works when dividing polynomials by what?
Binomial or Linear Term
This Theorem says that all polynomials are guaranteed to have at least 1 Complex root?
Fundamental Theorem of Algebra
How many Zeros, at most, can a 10th degree polynomial have?
10
Factor the following Quadratic using only Real Numbers.
y = 2x2 + 5x + 10
Un-factorable
What theorem says that if f(a) is positive and f(b) is negative that a zero must exist between x = a and x = b?
Intermediate Value Theorem
A Quintic divided by a Quartic would yield what type of polynomial?
Linear
What is the term used to compare the imaginary numbers below
(4 + 2i) (4 - 2i)
Complex Conjugate
Describe the end behavior (left and right) of a 7th degree polynomial with a negative leading coefficient.
Infinity on the left, Negative Infinity on the right.
What is the y-intercept of the polynomial below?
y = (2x + 4) (x - 3) (x + 4)2
-192
How does a zero with even multiplicity appear when graphed?
The polynomial touches but doesn't cross at the value.
Explain whether or not (x + 4) is a factor of the following polynomial and how you know.
f(x) = 2x4 + 5x3 - x2 + 1
26/17 + 19i/17
State, in your own words, what the Intermediate Value Theorem means.
A polynomial must touch all possible numbers between any two points.
What is the end behavior (left and right) of the polynomial below?
f(x) = -3x(2x + 5)(-x + 2)(5x - 4)2
Negative Infinity on the left and Positive Infinity on the right
Write the 4th degree polynomial in expanded form which contains the roots 3i and -2i.
y = x4 + 13x2 + 36
Divide the polynomial below by (7p - 10)
(-65p2 + 16p4 + 20 + 28p5 +36p - 59p3)
4p4 + 8p3 + 3p2 - 5p - 2
Use the given zero to fully factor the polynomial below, including complex factors, and write in factored form.
f(x) = x3 + 4x2 + 14x + 20 given a zero at
x = -1 - 3i
f(x) = (x + 2)(x - (-1-3i))(x - (-1+3i))