Consider the polynomials
(ab2+ 3ab+ 8a2) (-5ab2)
use the polynomials to illustrate the following:
a. polynomials are closed under addition
b. polynomials are closed under subtraction
c. polynomials are closed under multiplication
d. polynomials are not closed under division

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See Discussion for details

Discussion:

Polynomials are closed with respect to an operation if applying that operation to them generates another polynomial

A.   ( ab^2 + 3ab + 8a^2)  +  ( - 5ab^2)  =

       -4ab^2 + 3ab + 8a^2    which is a polynomial

B.   ( ab^2 + 3ab + 8a^2)  -  ( - 5ab^2)  =

       6ab^2 + 3ab + 8a^2    which is a polynomial

C.   ( ab^2 + 3ab + 8a^2)  *  ( - 5ab^2)  =

       -5a^2b^4 - 15a^2b^3 = 40a^3b^2  which is a polynomial

D  ( ab^2 + 3ab + 8a^2)  /  ( - 5ab^2)  =

     -(1/5) + 3(-1/5) (1/b) + 8 ( -1/5)a(1/b^2)

    which is NOT a polynomial because of the (1/b), ( 1/b^2)  terms

Thank you,

MrB

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc