Polynomial Function
The degree of the name "constant"
Ex. 4
What is 0
End behavior if a is positive and n is even
up and up
Write in factored form
x^3-2x^2-15x
x(x-5)(x+3)
What are the real or imaginary solutions?
2x^3-5x^2=3x
x=0
x=3
x=-1/2
What is the quotient and remainder of
x^3-14x^2+51x-54 by x+2
Q: x^2-16x+83
R:-220
The degree of the name "linear"
Ex. x+5
What is 1
End behavior if a is negative and n is even
down and down
Writing a Polynomial Factored Form
x^3-x^2-12x
x(x-4)(x+3)
What are the real or imaginary solutions?
x^5+4x^3=5x^4-2x^3
x=0
x=2
x=3
What is the quotient and remainder of
x^3-57x+56 by x-7
Quotient: x^2+7x-8
R: 0
The degree of the name "cubic"
Ex. 4x^3-2x^2+x
3
End behavior if a is negative and n is odd
up and down
Write a polynomial function in standard form with the given zeros:
-2, 2, and 3
P(x)=x^3-3x^2-4x+12
How would you factor out a GCF of
15x^4-20x^3=35x^2
5x^2(3x^2-4x+7)
If you divide a polynomial P(x) by x-a, then the remainder is
P(a)
The degree of the name "quadratic"
Ex. 3x^2
2
End behavior if a is positive and n is odd
down and up
Write a polynomial function in standard form with the given zeros:
3 and -3
P(x)=x^2-9
What are the real or imaginary solutions of the polynomial equation?
x^4=16
x=2
x=-2
x=+-2i
Given P(x)=x^5-2x^3-x^2+2,
what is P(3)?
P(3)=182
The degree of the name "quartic"
Ex: 2x^4+5x^2
4
End behavior of y=4x^3-3x
leading term: 4x^3
down and up: a=4 n=3
Write a polynomial function in standard form with the given zeros:
3,3, and -3
P(x)=x^3-3x^2-9x+27
What are the real or imaginary solutions of the polynomial equation?
x(x^2+8)=8(x+1)
x=2
x=-1+-i square root 3
Given P(x)=x^5-3x^4-18x^3+5x+20
what is P(-4)
P(-4)=-640