Express algebraically.

Length is 3x - 4, area is 6x^(4) +9x^(2)-3x-12
Simplify answer completely.

2 answers

The formula for the area of a rectangle is length times width. In this case, we have the length, 3x - 4, and the area, 6x^(4) + 9x^(2) - 3x - 12. We can set up the equation:

(3x - 4) * width = 6x^(4) + 9x^(2) - 3x - 12

To find the width, we can divide both sides by 3x - 4:

width = (6x^(4) + 9x^(2) - 3x - 12) / (3x - 4)

Now we can simplify the expression for width:

width = (2x^(2) + 3)(3x^(2) - 2) / (3x - 4)

Therefore, the algebraic expression for the width is (2x^(2) + 3)(3x^(2) - 2) / (3x - 4).
(6x^4 + 9x^2 - 3x - 12) รท (3x - 4)
= ...

I was expecting this division to be exact, but it is not.
Do a long division, and whatever the answer is, is your length