Am I a Polynomial?
Which of these would NOT be a polynomial function? (you can have more than one)
a) a quadratic function b) a cubic function
c) a linear function d) a square root function
e) an absolute value function
What are d and e?
The remainder when you divide 175 by 3.
What is 1?
The factored form of an equation of a polynomial function where both ends point downward and having zeros at -5, -2, (both multiplicity 1) and 5 (having multiplicity 2).
What is
f(x)=-(x+5)(x+2)(x-5)^2 ?
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, 2+3i, 2-3i, 4, and 0
What is 5th degree?
5+2i is a zero so _________ also has to be a zero.
What is 5-2i?
What is the name (type) of this polynomial?
f(x) = x^5+3x^2-4
What is a Quintic?
What is the remainder when you use long division to divide ?:
(6x^2+5x-10)/(2x+3)
What is -4
Given that (x-1) is a factor, the complete factored form of
p(x)=x^3-9x^2+23x-15
What is
p(x)=(x-1)(x-3)(x-5)
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?
Which of these functions is not a polynomial?
a) f(x) = x+1
b)f(x) = x^-2+3
c)f(x)=5x^3-2x^2+5
d)f(x)=4
e)f(x)=-4x^100
What is b?
What is the quotient when you divide?:
(3x^4-2x^2-5)/(3x^2-5)
What is
x^2+1?
Given -4 is a zero of
p(x)=4x^3+x^2-51x+36
all the other zeros are...
What are 3/4 and 3?
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 the three 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 of the following statements are MUST be true about a 5th degree polynomial with a negative leading coefficient?
a) It will always have five x-intercepts.
b) Both ends will be pointing downward.
c) It could have five turning points.
d) It will always cross the x-axis at least one time.
What is d?
What is the quotient when you divide?:
(x^5+x^4+2x+2)/(x+1)
What is
x^4+2
If -1 is a zero give the complete factored form of
f(x)=2x^3+7x^2+2x-3
What is
f(x)=(x+3)(x+1)(2x-1)
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 ?
On a mini-whiteboard sketch the graph of a fourth degree polynomial with a positive leading coefficient and exactly one real root with a multiplicity of 2.
? Mr. Brewer will decide if your graph is correct?
Which of the following statements are true about a 4th degree polynomial with a negative leading coefficient?
a) It might not ever cross the x-axis.
b) It could have two double roots.
c) Both ends will always be pointing in downward.
d) It might have three turning points.
What are a, b, c and d.
The length of a rectangle given A is its area and w is its width.
A=x^2+8x+15, w=x+3
What x + 5 ?
The remainder when dividing?:
(-x^9-1)/(x+1)
What is 0?
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 the -2 is a zero, find the zeros of
f(x)=x^3+2x^2+4x+8
What is +/- 2i and -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 ?