Am I a Polynomial?
Which of these would NOT be a polynomial function?
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 and 5i (might be a "trickster")
What is 3rd degree?
Which of these algebraic expressions are not polynomials?
a) 5/x
b) x^(1/3)
c) -4x^2
d) x/5
What are a and b
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 statements is always true about polynomial functions.
a) They continue infinitely up and down.
b) They always have a maximum or a minimum value.
c) Their ends always go in opposite directions.
d) Sometimes the ends loop around and meet eachother.
e) The leading coefficient is always plus or minus 1.
f) None of these is always true.
What is f?
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 two of the zeros are 0 and i
What is
f(x)=-2x^3-2x
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 ?
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 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)