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Polynomials Vocabulary
Write equations in Factored Form given Roots
Factoring Polynomials
Remainer Theorem
Muñoz Lore
100

What is a constant?

The term without any variables.

100
Roots at x = 2 and x = -3


Both have multiplicity of 1.

f(x) = (x-2)(x+3)

100

Factor completely.

f(x) = x2-9

(x+3)(x-3)

100

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. 

100

What sport did Muñoz play in high school?

Baseball

200

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.

200

Roots at x = 1, 2, and 0.


Multiplicity at x = 1 is 2. 

(x-1)2(x-2)(x)

200

Factor completely.

f(x) = x2+10x+25

(x+5)2

200

Is the following a factor of the polynomial?

(x+2) and x4+8x3+24x2+32x+16

Yes, the remainder is 0. 

200

Name 3 of Muñoz hobbies.




Results will vary.

300

The solutions to a polynomial are often referred to as this...

The x-intercepts are the solutions.

300

Roots at -2i and 3i

(x-2i)(x+2i)(x-3i)(x+3i)

300

Factor completely.


f(x) = 3x2+14x-24

(3x-4)(x+6)

300

Is the following a factor of the polynomial?


(x-2) of f(x) = 4x4-25x2+36


Yes, the remainder is 0.

300

300 points for each one you get right.

Name Mr. Muñoz 3 favorite sports teams.

NBA / MLB / NFL. 

Lakers / Giants / 49ers

400

How many solutions (roots / factors) does a polynomial have if the degree of the polynomial is equal to n?

N solutions.

400

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))

400

Factor completely


f(x) = x2-2x+2

(x-(1+i))(x-(1-i))

400

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.

400

What is Mr. Muñoz favorite Disney movie?

Will accept : Coco or Mulan

500

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.

500

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)

500

Factor completely


f(x) = 4x3-8x2-9x+18

f(x) = (x-2)(2x+3)(2x-3)

500

Is the following a factor of the polynomial?

(x+1) of f(x) = 4x5 + 4x4-25x3-25x2+36x+36


Yes, the remainder is 0.

500

Name Mr. Muñoz Niece.

Double points : 

Name his nephew.

Natalia / Sebastian