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.