A board has length (3x^4 + 6x^2 -18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length.
a. Find the length of each piece.
b. Find the area of each piece.
c. Find the area of the board before it is cut.
d. How is the area of each piece of the board related to the area of the board before it is cut?
length = (3x^4 + 6x^2 -18) meters width = 2x + 1 meters
total length = 3x^4 + 6x^2 - 18
length of each of three pieces = (3x^4 + 6x^2 - 18)/3
= x^4 + 2x^2 - 6
Area of each piece = width * length of the piece
= (2x + 1)(x^4 + 2x^2 - 6)
= 2x^5 + x^4 + 4x^3 + 2x^2 - 12x - 6
Area of the whole board = width * length of the board
= (2x + 1)(3x^4 + 6x^2 - 18)
= 6x^5 + 3x^4 + 12x^3 + 6x^2 - 36x - 18
The area of the each piece is one-third of the area of the whole board.
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