Polynomial Functions
A constant polynomial that consists of only a constant term, such as the polynomial 12 is called...
constant polynomial
Describe how to find all possible rational zeros.
Rational zero test.
Factors of constant divided by the factors of leading coefficient.
What does the remainder theorem do?
states that if a polynomial f(x) is divided by a linear expression x - c, the remainder r is equal to the value of the function evaluated at c, written as f(c)
Find a possible polynomial in factored form such that 1(with multiplicity 3), -2, and 5 are zeros.
f(x)=(x-1)^3(x+2)(x-5)
What is the leading coefficient of
6x^7+4x^3+5x^2-7x+10
6
Find the zeros of the following function.
f(x) = 3x^2(x-4)(x^2-4)(2x+5)
0, 4, +-2, -5/2
ONE 1
Find zeros:
f(x)=x^2-6x+13
The zeros are: 3+2i and 3-2i
Use synthetic division to divide
x^5+5x^4+6x^3-x^2+4x=29
by x+3
x^4+2x^3-x+7
Find rational zeros of
f(x)=2x^4+x^3-17x^2-4x+6
-3, 1/2
Give an example of an equation with a degree of 5 that has 3 real zeros
TBD
Find a polynomial with zeros at 2 and 3+i.
f(x)=x^3-8x^2+22x-20
If multiplicity of a zero is odd, the graph crosses what axis?
x-axis
Find all zeros given that -4 is a zero.
f(x)= x^4+x^3-14x^2-2x+24
+- sqrt(2) , 3, -4
How many possible relative extrema and possible zeros
(x^2+2x+1)
n=2 zeros
n-1=1 relative extrema
Find
i^54
-1
Find the possible rational zeros of
f(x)=x^4-5x^3+4x^2+2x-8
over the set of real numbers.
The possible rational zeros are factors of 8.
+-1, +-2, +-4, +-8
If the multiplicity is even, what does the graph do at that value?
Touches, does not cross the x-axis
Find all real zeros
f(x)=x^3-3x^2+2x-6
3
Multiplying a complex number by i on the complex plane geometrically represents a counterclockwise rotation of this exact number of degrees about the origin.
90 degrees
Put
(3+4i)/(1+2i)
in a+bi form.
11/5- 2/5i
Completely factor
f(x)=x^4-5x^3+4x^2+2x-8
over the set of complex numbers.
The complex factors are: x-(1+i) and x-(1-i)