Answer:
(3x-4) by (3x+2) or (-3x+4) by (-3x-2)
Explanation:
To factor 9x^2-6x-8 we want to find the factors of 9 and the factors of -8 that when multiplied in sequence and then added give us -6.
factors of -8:
-8 & 1
8 & -1
-4 & 2
4 & -2
you might also want to remember that these can be flipped, so if you have -8 & 1 you can also have 1 &-8.
factors of 9:
9 & 1
-9 & -1
3 & 3
-3 & -3
So now we just need to find numbers where
a & b are factors of 9 and c & d are factors of -8 and a*c+b*d=-6,
if that is the case then (ax+c)*(bx+d)=9x^2-6x-8
guess: 3 & 3 and -4 & 2
3*(-4) + 3*2=-12 +6 = -6
so one factoring is (3x-4)*(3x+2)
This means that one of the possible dimensions of the blanket is (3x-4) by (3x+2)
guess: -3 & -3 and 4 & -2
(-3)*4+(-3)*(-2)= -12+6 = -6
so another factoring is (-3x+4)*(-3x-2)
So you could also have a blanket with dimensions (-3x+4) by (-3x-2) but this might not make sense to do because, if you input positive numbers for x you will get negative dimensions which in the real world don't exist for a knitted blanket.
p.s sorry for the late response.