The expression that represents the area of the rectangle is 6x² + 29x + 35. The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
Let W be the rectangle's width and L its length.
Area of the rectangle = L × W square units
The sides of a rectangle are (2x + 5) units and (3x + 7) units, respectively. Then the area of the rectangle will be given as,
A = (2x + 5)(3x + 7)
A = 2x(3x + 7) + 5(3x + 7)
A = 6x² + 14x + 15x + 35
A = 6x² + 29x + 35
The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.
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Answer:
[tex]\textsf{A.} \quad \textsf{Area}=(2x+5)(3x+7)[/tex]
B. Degree = 2.
Classification = Quadratic trinomial.
C. Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
Step-by-step explanation:
Area of a rectangle
[tex]\boxed{A=lw}[/tex]
where l is the length and w is the width.
Given that a rectangle has sides measuring (2x + 5) units and (3x + 7) units, the area can be expressed as a product of the two sides:
[tex]\implies \textsf{Area}=(2x+5)(3x+7)[/tex]
FOIL method
[tex]\boxed{(a + b)(c + d) = ac + ad + bc + bd}[/tex]
Expand the brackets of the equation found in part A by using the FOIL method:
[tex]\implies \textsf{Area}=6x^2+14x+15x+35[/tex]
[tex]\implies \textsf{Area}=6x^2+29x+35[/tex]
The degree of a polynomial is the highest power of a variable in the polynomial equation. Therefore:
A polynomial is classified according to the number of terms and its degree.
Closure property under Multiplication
A set is closed under multiplication when we perform that operation on elements of the set and the answer is also in the set.
Therefore, Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).
