Standard Form/Classifying
What is the degree of the following polynomial?
2x3
cubic
Describe the end behavior
y = 4x + x3
down and up
What are the zeros of y = ( x + 2 ) ( x - 3)
- 2 and 3
factor:
x3 + 64 = 0
( x + 4 ) ( x2 - 4x + 16) = 0
According to the factor theorem, if the root of a polynomial function is r, then the factor is ( x -r ) or ( x + r)?
( x - r)
classify this polynomial acc to the number of terms?
5a3 - 6a
binomial
Describe the end behavior
y = 3x - 2x3 -1
up and down
What are the zeros of y = x ( x - 2) ( x + 5)
0 , 2 , -5
Factor : 2x3- 250 = 0
2 ( x - 5 ) ( x2 + 5x + 25) = 0
Factor x4- x2
x2 (x2 -1 )
= x2 (x -1 )( x + 1 )
What is the degree of the following polynomial?
-6a4 + 10a6
6th degree
Describe the end behavior
y = 5x3 + 6x2 - 4x3 - x3
up and up
What are the factors of y = x3 - 2x2 + x?
factor : 27x3 + 1 = 0
The side of a cube measures 3x +2 units long. Express the volume of the cube as a polynomial
27x3 + 54x2 + 36x + 8
What is the leading coefficient of the polynomial below?
k + 1 -10k3
-10
If the end behavior is up and down...what is the sign of the coefficient and what is the degree ( even/odd) ?
negative & odd
Write the polynomial function with zeros 1,1,2
y = x3 - 4x2 + 5x -2
Factor then solve
x4 - 12x2 + 11=0
( x + 1) ( x - 1) ( x2 - 11 ) = 0
x = -1, 1, - /+ square root 11
Your friend claims that the zeros of 3x3 + 7x2 - 22x - 8 = 0
are -4, 2, and -1. What did your friend do wrong? What are the correct zeros?
Your friend forgot to divide by 3 when solving an equation to find the third factor. The correct zeros are -4, 2, and - 1/3 .
What is the degree AND leading coefficient of the polynomial below?
4x - 9x2 + 4x3 - 5x4
Degree=quartic
Leading coefficient=-5
If the end behavior is up and up...what is the sign of the coefficient and what is the degree ( even/odd) ?
positive & even
Write the polynomial function in factored form given the zeros 2 , -7 with multiplicity of 3
y = ( x - 2 ) ( x + 7)3
Factor then Solve
x4 + 13x2 + 36 = 0
( x2+ 4) ( x2 + 9 ) = 0
-2i , 2i, 3i , -3i
Your mother is 25 years older than you. Your father is 3 years older than your mother. The product of all three ages is 32,130. How old is your father?
45 years old