Question

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.

I especially need help with a!

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?

Answer 1

a. x^4 +2x^2 -6

b. 2x^5 +x^4 +4x^3 +2x^2 -12x -6

c. 6x^5 +3x^4 +12x^3 +6x^2 -36x -18

d. the area of one piece is 1/3 the area of the board

Explanation:

a. The length of each piece will be 1/3 the length of the board. Divide each of the coefficients of the length polynomial by 3:

piece length = (1/3)(board length) = (1/3)(3x^4 +6x^2 -18) = x^4 +2x^2 -6

__

b. The area is the product of length and width.

piece area = (width)×(piece length) = (2x +1)(x^4 +2x^2 -6)

piece area = 2x^5 +x^4 +4x^3 +2x^2 -12x -6

__

d. The board area is 3 times the area of one piece. The area of one piece is 1/3 the area of the board.

__

c. board area = 3×(piece area) = 6x^5 +3x^4 +12x^3 +6x^2 -36x -18