A graphic arts company creates posters with areas that are given by the equation.

Question

A graphic arts company creates posters with areas that are given by the equation . 𝐴 = 2𝑥 2 + 11𝑥 + 12 a) Write expressions for possible dimensions of the posters. b) Write expressions for the dimensions of a poster whose width is doubled and whose length is increased by 2. Write the new area equation as a simplified polynomial.

Answer 1

2x^2 +11x +12 = Area = Length times Width

= (2x+3)(x+4) = Length times Width

possible dimensions: 3 by 4, 5 by 5, 11 by 6

for x = 0, 1 or 2

Length = 2x+3, Width = x+4

x>-4 and x>-3/2 to keep the dimensions >0

Area >0

double Width, increase Length by 2

L=2x+3+2 = 2x+5

W=2(x+4) = 2x+8

Area = A = (2x+5)(2x+8) = 4x^2 +26x +40

A= 4x^2 +26x +40

x>-3/2

new Area > 4(3/2)^2 -26(3/2)+40 = 9-39+40=10

new Area >10

possible dimensions: 5 by 8, 7 by 10, 9 by 12

if x=0,1 or 2