Polynomial Basics
Roots and FTA
Polynomial Graphs
Solving Quadratics
Random
100
Can a linear expression (3x + 1) be considered a polynomial?
Yes
100
"Roots" is a word that is used to describe what about a polynomial?
Values of variable that make it equal 0; solutions to polynomial equation
100
What word is used to describe the shape of a quadratic polynomial graph?
Parabola
100
What are the solutions to the equation 4x^2 = 64?
x = 4, x = -4
100
True or false: All constant functions are polynomials.
True
200
What term is used to classify the polynomial based on the highest value of its variable?
Degree
200
According to the FTA, how many complex roots will a given polynomial have?
Number equal to its degree
200
Functions that have a general "S" type shape will be polynomials of what type of degree?
Odd degree
200
What are the solutions to the quadratic equation given by (2x-3)(4x+1) = 0?
x = 3/2; x = -1/4
200
How many times will a polynomial graph with no real solutions cross the x-axis?
None
300
In the polynomial 4x^2 + 3x - 1, 4 is considered the...
Leading coefficient
300
If a polynomial is written in the form (x-a)(x+b)(x-c) = 0, how many roots will it have?
Three
300
Polynomial functions of even degree exhibit what type of symmetry?
Even symmetry; symmetry to y-axis
300
Find the solutions of the quadratic equation x^2 + 10x + 21 = 0
x = -3, x = -7
300
If a complex number a + bi is a solution to a polynomial function, then what must also be another known solution?
Its conjugate, a - bi
400
Give an example of a fifth degree polynomial with three terms.
Answers may vary; Dan will judge
400
A fourth degree polynomial has a graph as given on the board. Describe how many complex and real roots the polynomial has.
Answer will vary based on graph given by Dan
400
Sketch an example of a fifth degree polynomial function with two real roots.
Answers may vary; Dan to judge
400
Find solutions for the quadratic equation: 5x^2 + 2x + 12 = 0
Dan to give answer on board
400
State the degree, number of complex roots, and number of real roots of the polynomial given by f(x) = (x-1)(x^2+2)(x^2-16)
Degree: 5 Real roots: x = 1, x = 4, x = -4 Complex roots: x = sqrt(2)i, x = -sqrt(2)i
500
Give the formal general form of a polynomial.
See board
500
Give all zeroes for this polynomial equation written on the board.
Answer will vary based on equation given by Dan
500
Draw a polynomial graph that could match the polynomial function: f(x) = (x-4)(x+2)(x^2+1)
Answers may vary; any quartic function with zeroes at x=4 and x=-2 may suffice (Dan to judge)
500
Solve the following quadratic equation by COMPLETING THE SQUARE: x^2 +4x - 1 = 0
x = 4 + sqrt(17) ; x = 4 - sqrt(17)
500
Give the polynomial equation whose zeroes would be 5, -4, 3i, and -3i.
x^4 - x^3 - 11x^2 - 9x -180
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