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.
What is continuity.
100
_____ of a rational function consists of all real numbers that aren't zeros of the denominator.
What is domain
100
Write the next 3 problems in a+bi form: (4+3i)-(8-6i)
What is -4+9i
100
Every nonconstant polynomial has a 0 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 point ______ the x-axis.
What is crosses.
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 real coefficients whose zeros include 2 and 3+i.
What is x^3-8x^2=22x-20
400
Is 2x^2+1 a factor of 6x^-4x^2+3x-2?
Yes.
400
When the absolute value of x is large, the graph of the polynomial function most closely resembles the graph of its highest degree term.
What is end behavior
400
What makes the denominator 0 makes the numerator 0.
What are holes
400
i^56
What is 1
400
Completely factor f(x)=x^4-5x^3+4x^2+2x-8
What is (x+1)(x-4)(x-(1+i))(x-(1-i))
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, plug in a 0 for every x.
What is y-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
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