A large square carpet is initially x inches long and x inche

A large square carpet is initially x inches long and x inches wide. Randy decides to trim 3 inches off each edge of the carpet because the edges are worn. Later he goes back and trims 4more inches off each edge.

(a) Express the final area (A) of the carpet in square inches (after both trim jobs) as a polynomial function of x.
A(x) =

(b) How many square inches of material were removed in the first trim job? Express the area removed in the first trim job (T₁) as a function of x.
T₁(x) =

(c) How many square inches of material were removed in the second trim job? Express the area removed in the second trim job (T₂) as a function of x.
T₂(x) =

Solution

Soultion:

Given that

Initial length of square is x inches

(a) Final area after both trim job = side * side = ( Area of square = side²⁾   

A(x) = (x-6) *(x-6)= x² -12x +36

(b) Area removed from fist trim = Initial area of square - remaining area of square after first trim

T1(x) = x² - (x-3) *(x-3) = x² -x² +6x-9

T1(x) = 6x -9

(c) Area removed from second trim = reamaining area after first trim - remaining area after 2nd trim

T2(x) = (x-3)² - (x-6)²

T2(x) = x²-6x+9 - x² +12x -36

T2(x) = 6x -27