Polynomial Functions
Graphs of Polynomial Fuctions
Rational Functions
Complex Numbers
Fundamental Theorem of Algebra
100
If a polynomial f(x) is divided by x-c, then the remainder is f(c).
What is the remainder theorem
100
Every graph of a polynomial function is continuous.
False.
100
The _____ of a rational function consists of all real numbers that don't create zeros in the denominator.
What is domain
100
(4+3i)-(8-6i)
What is -4+9i
100
Every polynomial has an x-intercept when graphed, even if some of the are in the complex number system.
What is the fundamental theorem of algebra
200
A polynomial of degree n has at most n distinct real zeros.
What are the zeros of a polynomial
200
If the multiplicity of a factor is odd, the x-intercept will ______ the x-axis.
What is cross through.
200
Find domain: 1/(x^2)
What is all real numbers but 0
200
(1+i)+(3-7i)
What is 4-6i
200
Find the zeros of f(x)=x^2-6x+13
What is 3+2i and 3-2i
300
The remainder when x^79+3x^24+5 is divided by x-1.
What is 9
300
The point where the graph crosses the x-axis.
What is an x-intercept.
300
Find domain: (x^2+3x+1)/(x^2-x-6)
What is x cannot equal 3 or -2
300
4i(2+.5i)
What is 2+8i
300
Find a polynomial with the factors:
400
Is 2x^2+1 a factor of 6x^3-4x^2+3x-2?
Yes.
400
When the absolute value of the coefficient of x is large, the graph of the polynomial function most closely resembles the graph of its highest degree term.
True
400
What you can never divide by.
What is zero?
400
i^56
What is 1
400
Completely factor:
What is
(x+3) (x+5)
500
A polynomial function f(x) has a linear factor x-a if and only if f(a)=0.
What is the factor theorem
500
Complete graphs show these three things.
What are intercepts, extrema, and behavior.
500
To find this, set each factor equal to zero.
What is the x-intercepts
500
i^55
What is -i
500
Find polynomial f(x) degree 5 such that 1, -2, and 5 are zeros, 1 is a zero of multiplicity 3 and f(2)=-24.
What is 2x^5-12x^4+4x^3+40x^2-54x+20