The factored form is (x - 8)(x + 2).
(x - 8)(x + 2)
x^2 + 2x - 8x - 16
x^2 - 6x - 16
If he used 34 bottles for every batch just divide 214 bottles he used by 34 it takes for a batch
he made 6.3 batches
Before I start, I wonder if we are missing some information? The question you posted says "He wanted to make another quilt"...does your question have any information about a first quilt that we need to take into consideration?
If not, and if this is all the information we have, then you start by knowing that the area of a rectangle (i.e., quilt) = length x width. So, to get a quilt with an area of 42, you need to find two numbers that multiply together to make 42. For example, 6 x 7 = 42, so the dimensions of the quilt could be 6 feet by 7 feet. Technically, 1 x 42 and 2 x 21 and 3 x 14 also = 42, so the quilt dimensions could also be 1 foot by 42 feet or 2 feet by 21 feet or 3 feet by 14 feet, but those would be a really unusual and awkward sizes for a quilt, so 6 feet by 7 feet is the better answer.
