Identify Characteristics of
Polynomials
Polynomials
What is the end behavior of the function?
(Show us with your arms!)
x4-3x2+2x-5
As x -> -oo, y -> oo
As x ->oo, y-> oo
Factor the polynomial
x3 - x2 - 12x
x(x - 4)(x - 3)
Solve the polynomial equation
x3-x2-30x = 0
x = -5, x = 0, x = 6
What is the degree and leading coefficient of the polynomial?
2x2-3x6+5x4+2-3x3-22x5
Degree: 6
Leading Coefficient: -3
Factor the polynomial
x3+27
(x + 3)(x2-3x+9)
Find all of the possible rational roots of the equation
6x3+2x2-4x+22
+-1, 2, 11, 22, 1/2, 11/2, 1/3, 2/3, 11/3, 22/3, 1/6, 11/6
Write the polynomial in standard form
4x2-3x+5x3-7
5x3+4x2-3x-7
Factor the polynomial
x3 - 3x2 + 4x - 12
(x - 3)(x2+4)
Write an equation given the roots
x = 2, x = 3 + i
f(x) = x3-8x2+21x-28
What type of polynomial is this?
x4-3x3+22x2-39x+24
Factor the polynomial
36x4-25
(6x2-5)(6x2+5)
Find all of the roots of the equation
f(x) = x3+x2-5x+3
What kind of roots do you have?
x = 1, x = 1, x = -3
x = 1 is a double root, x = -3 is a single root
What is the end behavior of an odd degree function with a negative leading coefficient?
(show us with your arms)
As x -> -oo, y -> oo
As x ->oo, y-> -oo
Is the binomial a factor of the polynomials?
f(x) = 3x3+7x2-8x-5
x + 5
No, the remainder does not = 0
Find all of the roots of the equation
f(x) = x4- 5x2 - 36
x = 3 and x = -3 are roots
x = 3, x = -3, x = 2i, x = -2i