Polynomials Review - G

What is the temperature?

100

Identify the degree of this monomial: 

-5x^2

Degree: 2

200

Identify the degree of this monomial

4

Degree: 0

300

Identify the degree of this polynomial

-7-x

Degree: 1

400

If a polynomial has 3 turning points, what is the minimal degree this polynomial could be?

Degree: 4

500

Identify the degree of this polynomial

-5x-7x^3+4x^2+3x^5

Degree: 5

Identifying Number of Terms

100

Identify the following polynomial from its number of terms:

-9

Monomial

200

Identify the following polynomial from its number of terms:

Binomial

300

Identify the following polynomial from its number of terms:

x^2-3x+1

Trinomial

400

Identify the following polynomial from its number of terms:

-6x+2x^2+x^3-2x^2+4x+4

Trinomial 

(x^3-2x+4)

500

Identify the following polynomial from its number of terms: 

((x-1)(x+1)(x^2-1)(x^2+1))+x^2

Trinomial 

(x^6-x^4-1)

Dividing Polynomials

100

x^2-1 divx-1

x+1

200

2x^3-3x^2+x-6 div(x-2)

2x^2+x+3

300

What is the remainder of:

2x^3-3x^2+x+11 div x-2

17

400

-x^4 +x^3+2x^2-3x+1 div (x^2-2x+1)

(-x^2-x+1)

500

5x^4-6x^3-8x^2+12x-4 div (x^2-2)

(5x^2-6x+2)

Multiplying Polynomials

100

Simplify:

(x-2)(x-2)

x^2-4x+4

200

Simplify:

(x^2-5x+7)(x-2)

x^3-7x^2+17x-14

300

Simplify:

(x-1)(x-2i)(x+2i)

x^3-x^2+4x-4

400

Find the degree 3 polynomial if the given zeros of that polynomial are:

x=2-sqrt(3)

x=3

x^3-5x^2+5x-1

500

Find the list of possible rational zeros of:

f(x) = 12x^3+14x^2+10x+8

+-(1, 2, 4, 8, 1/2, 1/3, 2/3, 4/3, 8/3, 1/4, 1/6, 1/12)

Theorems

100

Making this list of ___________ __________ zeros will help you figure out what values are in fact the zeros of a polynomial.

Take the factors of the Leading Coefficient and divide them by the factors of the constant

Possible Rational 

200

This theorem says that if x=a+bi is a root, then x=a-bi is also a root.

Conjugate Roots Theorem

300

This theorem states the remainder of the division

f(x)/(x-a) = f(a)

Remainder Theorem

400

If

f(a) = 0

Then  (x-a) is a factor of f(x)

The Factor Theorem

500

The number of solutions to a polynomial equation is exactly equal to the degree

Fundamental Theorem of Algebra

Degree names

100

Identify this polynomial based off of its degree:

2x^2-x+5

Quadratic Polynomial (degree 2)

200

Identify this polynomial based off of its degree:

-5

Constant Polynomial (degree 0)

300

Identify this polynomial based off of its degree: 

1+x+2x^2+3x^3+4x^4

Quartic Polynomial (degree 4)

400

Identify this polynomial based off of its degree: 

(x^2-1)(x-5)

Cubic Polynomial (degree 3)

500

Identify this polynomial based off of its degree:

-2x^7+4x^5-2x^5+2x^7+x^3

Quintic Polynomial (degree 5)