Part A: Create a fifth-degree polynomial in standard form. How do you know it is in standard form? (5 points) Part B: Explain the closure property as it relates to addition of polynomials. Give an example. (5 points)

(10 points)

A. A fifth degree polynomial is defined by .

B. The closure property in relation to addition of polynomials is defined by following expression:

, ,

For   and , we know that .

Step-by-step explanation:

A. A polynomial is in standard form if and only if is written in the following form:

, (1)

Where:

- Grade of the i-th monomial.

- Grade of the polynomial.

- i-th coefficient of the polynomial.

Then, a fifth degree polynomial in standard form is:

(3)

B. The closure property in relation to addition of polynomials is defined by following expression:

, , (3)

Let proceed to demonstrate this closure property for every polynomial:

1) Given.

2) Sum property/Associative property.

3) Sum property/Result.

Let consider that and , then we know by closure property for addition of polynomials that:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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