Polynomials Vocabulary
What is a constant?
The term without any variables.
Both have multiplicity of 1.
f(x) = (x-2)(x+3)
Factor completely.
f(x) = x2-9
(x+3)(x-3)
Is the following a factor of the polynomial?
(x-3) and f(x) = 2x3-3x2+7x-2
No, the remainder is not equal to zero.
What sport did Muñoz play in high school?
Baseball
What is the difference between a root and a factor?
Root is where the graph has an x-intercept.
A factor is a polynomial which divides another polynomial.
Roots at x = 1, 2, and 0.
Multiplicity at x = 1 is 2.
(x-1)2(x-2)(x)
Factor completely.
f(x) = x2+10x+25
(x+5)2
Is the following a factor of the polynomial?
(x+2) and x4+8x3+24x2+32x+16
Yes, the remainder is 0.
Name 3 of Muñoz hobbies.
Results will vary.
The solutions to a polynomial are often referred to as this...
The x-intercepts are the solutions.
Roots at -2i and 3i
(x-2i)(x+2i)(x-3i)(x+3i)
Factor completely.
f(x) = 3x2+14x-24
(3x-4)(x+6)
Is the following a factor of the polynomial?
(x-2) of f(x) = 4x4-25x2+36
Yes, the remainder is 0.
300 points for each one you get right.
Name Mr. Muñoz 3 favorite sports teams.
NBA / MLB / NFL.
Lakers / Giants / 49ers
How many solutions (roots / factors) does a polynomial have if the degree of the polynomial is equal to n?
N solutions.
Roots at x = 1 , 2, -2, and 5-i
All multiplicities of 1.
(x-1)(x-2)(x+2)(x-(5-i))(x-(5+i))
Factor completely
f(x) = x2-2x+2
(x-(1+i))(x-(1-i))
Is the following a factor of the polynomial?
(x-1) of f(x) = 4x5 + 4x4-25x3-25x2+36x+36
No, the remainder is not equal to 0.
What is Mr. Muñoz favorite Disney movie?
Will accept : Coco or Mulan
True or False :
The following polynomial is guaranteed to have imaginary solutions.
f(x) = 4x4+7x2+100
True.
Any polynomial of even degree and only that is only positive will be guaranteed to have imaginary solutions.
Roots at x = r, s, t, u.
r has a multiplicity of 7
s has a multiplicity of 2
t has a multiplicity of n
u has a multiplicity of 1
(x-r)7(x-s)2(x-t)n(x-1)
Factor completely
f(x) = 4x3-8x2-9x+18
f(x) = (x-2)(2x+3)(2x-3)
Is the following a factor of the polynomial?
(x+1) of f(x) = 4x5 + 4x4-25x3-25x2+36x+36
Yes, the remainder is 0.
Name Mr. Muñoz Niece.
Double points :
Name his nephew.
Natalia / Sebastian