Let S=20x²-27x-8: the area, L=4x+1: the length, and W=the width, so you have:
S=LW Substitute the equation given for S and L, getting
20x²-27x-8=(4x+1)W* The left side is quadratic, but (4x+1) is linear, so W must be linear.
Let W=ax+b, so 20x²-27x-8=(4x+1)(ax+b)=4ax²+(4b+a)x+b. We have:
4a=20 and b=-8, so we have: a=5 and b=-8 Thus, W=5x-8
CK: 4b+a=4x(-8)+(5)=-27 CKD.
Therefore the width is: 5x-8
* We can factor this using long division: 20x²-27x-8=5x(4x+1)-5x-27x-8=5x(4x+1)-32x-8
=5x(4x+1)-8(4x+1)=(4x+1)(5x-8) We have: W=5x-8