For f(x)=4x+1 and g(x)=(x^2)-5, find (f-g)(x).

Part A: (12x² +74x + 44) Square units.

Part B: A Second ( 2nd ) Degree Trinomial

Part C: Part A which is the multiplication of 6x + 4) units and (2x + 11) units to find the Area of a rectangle demonstrate closure property because it is the multiplication of two Binomials to give us a second degree Trinomial which is

(12x² +74x+ 44) Square units.

Step-by-step explanation:

Part A: What is the expression that represents the area of the rectangle?

The formula for the Area of a rectangle is given as Length × Breadth

We are told in the question that rectangle has sides of (6x + 4) units and (2x + 11) units

Therefore, Area of the rectangle is calculated as:

(6x + 4) units × (2x + 11) units

6x(2x +11) + 4(2x + 11)

12x² + 66x + 8x + 44

(12x² +74x+ 44) Square units.

Part B: What are the degree and classification of the expression obtained in Part A?

A polynomial can be defined as a mathematically expression that consists of one or more than one algebraic terms in it. One of the characteristics of a polynomial is the degree is carries. The degree of a polynomial can be defined as one of algebraic terms that carries the highest exponential values.

For example

4x⁴ + 2x³ + 5x² + 1 : The degree of this polynomial is 4 because the algebraic term with the highest exponential values is "4x⁴".

A polynomial can be classified into 3 types based on the number of terms that it contains.

a) A monomial : = 7x

b) A Binomial = 6x² + 4

c) A Trinomial = 3x³ + 2x + 1

Hence, for the above question, the degree and classification of the expression obtained in Part A which is

(12x² +74x + 44) Square units is that it is a second (2nd ) degree Trinomial. This is because it consists of 3 terms and the algebraic terms with the highest exponential values is 12x².

Part C: How does Part A demonstrate the closure property for polynomials?

Closure property for polynomials is one of the characteristics that a polynomial shows when it undergoes either Addition, Subtraction or Multiplication in other to give us another polynomial.

Therefore, in the question above,

Part A which is the multiplication of 6x + 4) units and (2x + 11) units to find the Area of a rectangle demonstrate closure property because it is the multiplication of two Binomials to give us a second degree Trinomial which is

(12x² +74x+ 44) Square units.