Question

The exponent rules are needed in order to perform operations on polynomials. In your own words:
Explain what a polynomial is and identify the different parts of a polynomial
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms- explain how foil helps us to accomplish this, and what category of polynomials foil applies to
There are two special case products where the product takes on special patterns- explain these two cases and when they occur
For each of the two special cases, illustrate your explanation with an appropriate exercise from the text (note the pg. and exercise number in your post), showing how the multiplication is performed using the special pattern formula, then also showing the same result using foil.

Answer 1

Questions:

1)Explain what a polynomial is and identify the different parts of a polynomial?

Polynomials are nothing but the sum of the variables and exponents.

they are generally written with its terms being ordered in decreasing order of exponents

let us say for example,

2x​5​​y​2​​−3xy​2​​−7

is a polynomial.

for the polynomial coefficients, take the numbers in front of each terms.

coefficients: 2,-3,-7

Leading coefficient here is 2

and the degree here add the exponent of the each term: 7,3,0

degree of the polynomial: it is the degree of the leading term that is 7

and the last part that is the constant which is -7

2) Explain the different labels used to categorize polynomials

classification of the polynomial as per

A)Degree

zero degree

first degree and so on

B)Coefficient

finished polynomial

incomplete polynomial

null polynomial

C) Degree of their monomoials

ordered

homogeneous

hetrogeneous

equal

3) Explain how addition and subtraction of polynomials is accomplished?

the addition/substraction of the two polynomial is quite simple

as you see here :

we only have privilage to answer three question at once

Thanks :)