To factor it completely you first look at the first term, if the a term is 1 then your good if it is not you need to divide it by whatever number to make the a term 1, in the first question the a term is just x^2 so it's good. Then,you focus on the b and c term, you have to find multiples of term C that adds up to term b. Going back to problem 1, c is 16 and b is 10. So the two factors would be 8 and 2,because 8×2=16 and 8+2=10. the final step is to put into the proper format, (x+2) (x+3), which would be considered completely factored.
A = L * W = 75 so L = 75/W Cost = 4W + 8(2L + W) = 4W + 16L + 8W = 12W + 16L = 12W + 1200/W C' = (12(W^2 - 100))/(W^2) = (12(W-10)(W+10))/(W^2) so W = 10 then L = 7.5
If the long side is 6 inches and it's 3x the length of the short side, then you need to divide the long side into 3 parts because the short side is 1/3 the length of the long side. This means that the short side is 2 inches.
