Exponents
Quadratics
Polynomial Operations
Imaginary Numbers
Polynomial Graphs
Composition of Functions
Extra Math
100
(2x^2)(3x^5)
6x^7
100
Factor:
x^2-5x+6
(x-6)(x+1)
100
3x^2(x+5)
3x^3+15x^2
100
What is
i^2
-1
100
How many x-intercepts are represented in this graph?
4
100
f(x)=2x and g(x)=6x
find
f(g(x))
f(g(x))=12x
100
A linear polynomial has exactly 1 real root, how many complex roots does it have?
0
200
(3x^5y^2)*(-4xy)
(-12x^6y^3)
200
Solve: x^2-16=0
x=4, x=-4
200
(2x^3+x^2+1)+(3x^3-2x^2+2x+2)
5x^3-x^2+2x+3
200
What is
(2+3i)-(5+2i)
-3-i
200
What is the degree of the polynomial in this figure?
Degree = 4
200
f(x)=x^2 and g(x)=sqrt(2x-1)
find
f(g(x))
f(g(x))=2x-1
200
A quartic polynomial has exactly 2 real roots, how many complex roots does it have?
2 complex roots
300
(16x^4)^(1/2)
4x^2
300
Solve:
2x^2-5x-7=0
(x+1)(2x-7)-> x=-1, x=7/2
300
What is
(3x^4+2x^3-x^2+1) -(5x^3+2x-5)
3x^4-3x^3-x^2-2x+6
300
What is
4i(2-i)
4+8i
300
Is the function a(x): even, odd, or neither
Even
300
Are f(x) and g(x) inverse functions given
f(x)=2x+5 and g(x)=(x-5)/2
Yes, they are inverses
300
What are the zeros and their multiplicities in the following function?
y=2x(x-1)^4(x-5)
x = 0 (m1)
x= 1 (m4)
x= 5 (m1)
400
(8x^4y^3)/(2xy^2)
4x^3y
400
What is the vertex of the parabola in the equation
y=3(x+1)^2-2
vertex = (-1,-2)
400
(2x+1)(x-4)
2x^2-7x-4
400
Solve
7x^2+28=0
2i, -2i
400
How many turning points are in this polynomial?
2 turning points
400
True or False: Two functions are inverses if their composition results in 2x.
That is, f(g(x))=2x
False
400
True or False: x-1 is a factor of
x^3-3x^2+3x-1 because the remainder is zero when divided by x-1.
True
500
(3x^3y^4)^2
9x^6y^8
500
What is the range of the function
y=-3(x-1)^2+3
(-inf, 3)
500
Use synthetic division to find the remainder when
(2x^3-2x^2+x-1)/(x-1)
Remainder is 0
500
Simplify: 2i^4+3i^2-5i+1
-5i
500
Given the leading coefficient in the polynomial is 1, write the equation of the polynomial displayed in the figure.
b(x)=x(x+2)(x-2)
500
Find the inverse of
f(x)=sqrt(2x-5)
f^-1(x)=(x^2+5)/2
500
What is the complex conjugate of 4-5i
4+5i
600
(2x^3)^-2/(xy^2)
1/(4x^7y^2)
600
What is the convexity (concave up
y=-3x^2-5x+1
/down)
Concave down
600
Find the quotient when
(3x^2-3x+4) is divided by (x+1)
3x-6 +10/(x+1)
600
Use the quadratic formula to solve
x^2+x+2=0
(-2 - sqrt(1^2-4(1)(2)))/2 and
(-2 + sqrt(1^2-4(1)(2)))/2 -->
(-2-isqrt(7))/2 and (-2+isqrt(7))/2
600
What is the end behavior of this graph as x -> inf?
b(x) goes to inf
600
What is the inverse of
f(x)=6x^2-5
f^-1(x)=sqrt((x+5)/6)
600
What are the domain and range of any odd degree polynomial function?
Both the domain and range are (-inf, inf).