Properties of Exponents
Evaluate the expression:
3^3 *3^-2
3
Find the sum:
(3s^3+s)+(4s^3-2s^2+7s+10)
7s^3-2s^2+8s+10
What is the end behavior of the following polynomial function?
f(x)=-2x^4-x^3+4x-5
Degree is even and leading coefficient is negative so both ends go down
Factor the polynomial completely:
30b^3-54b^2
6b^2(5b-9)
What are the two features of a polynomial used to define it?
Degree and Number of terms
Evaluate the expression:
5^2/5^3
1/125
Find the difference:
(4t^3-11t^2+4t)-(-7t^2-5t+8)
4t^3-4t^2+9t-8
What is the end behavior of the following polynomial function?
f(x)=-5x^3+3x^2-x+7
The degree is odd and the leading coefficient is negative so it is up to the left and down to the right
Factor the polynomial completely:
z^3-6z^2-72z
z(z-12)(z+6)
What is the Fundamental Theorem of Algebra (It regards the number of zeros)
The degree of a polynomial is equivalent to the number of zeros that polynomial has.
Simplify the expression:
(2^2y^3)^5
1024y^15
Find the product:
(y-7)(y+6)
y^2-x-35
How many zeros does the following function have?
f(x)=-x^3+x^2+3x-3
The degree is 3 so this function has 3 zeros.
Factor the polynomial completely:
n^3+5n^2-9n-45
(n-3)(n+3)(n+5)
What is the rule about irrational and complex zeros?
If an irrational number is a zero of a polynomial, its' conjugate is also a zero of the polynomial. If a complex number is a zero of a polynomial, its' conjugate is also a zero of the polynomial
Simplify the expression:
(2a^3b^-4)/(3a^5b^-2
2/(3a^2b^2
Find the product:
(x-4)^3
x^3-12x^2+48x-64
How many x-intercepts does the following function have?
f(x)=2(x+2)^2(x+4)^2
The degree of the polynomial is 4, so there are 4 zeros. However, they are repeated zeros so there are only two x-intercepts
Factor the polynomial completely:
15x^5-72x^3-108x
3x(x^2-6)(5x^2+6)
Why is the number of zeros a polynomial has not always equivalent to the number of x-intercepts the polynomial has.
Repeated Zeros or Complex Solutions
Simplify the expression:
(x^2y^-3)/(3y^2) * y^2/x^-4
x^6/(3y^3)
Find the product:
(3q-8)(-9q+2)(q-2)
-27q^3+132q^2-172q+32
Graph the following function:
f(x)=(x+1)^2(x-1)(x-3)
See Graph
Factor the polynomial completely:
g(x)=2x^3-7x^2+9
(x-1)(2x-3)(x-3)
What is the rational zero test?
A way to test for all rational zeros of a polynomial function. Take the factors of the constant term divided by the factors of the leading coefficient.