Answer:
[tex]l=3x^2-4x+1[/tex]
Step-by-step explanation:
Given that,
The area of a rectangle is, [tex]A=3x^3+14x^2-23x+6[/tex]
The width of the rectangle, b = (x+6)
We need to find the expression for the length of the rectangle. We know that, the area of a rectangle is given by :
A = lb
Where
l is the length of the rectangle
Put all the values,
[tex]l=\dfrac{A}{b}\\\\l=\dfrac{3x^3+14x^2-23x+6}{(x+6)}\\\\l=\dfrac{(x-1)(x+6)(3x-1)}{(x+6)}\\\\l=(x-1)(3x-1)\\\\=3x^2-4x+1[/tex]
So, the length of the rectangle is equal to [tex]3x^2-4x+1[/tex].
