Please help!! i need to know how to solve and understand this.

Question

The area, in square units, of a rectangle is represented by 6^3-2x^2+4x.If the width, in units, is 2x, what is the length, in units?

Answer 1

Good evening,

I think your equation was supposed to be 6x³-2x²+4x?

Let's start with the basics: How do you calculate the area of a rectangle?

Length x Width = Area of Rectangle

The problem gives you the width, and the area. They aren't listed as whole numbers (they are written with variables) so while you can't directly calculate the actual length, width, or area, you can still do some number crunching. Remember, any time you have an equation and you can fill in all but one blank, you can solve for the remaining blank.

Length x Width = Area of Rectangle

Length x 2x = 6x³-2x²+4x

If this equation had simply been: Length x 2 = 10, you would instinctively know that you divide both sides of the equation by two. Just because there are variables in the equation doesn't change how you do the math. Instead of dividing by 2, we are dividing by 2x.

But what do we divide by the 2x? The 6x³? The -2x²? Or the 4x?

The answer is: All of the above. When you are dividing (or multiplying for that matter) any polynomial, you must do the operation to all of the pieces, not just whichever you feel like. I'll leave the number crunching to you, but just ask this:

What do you get when you do the following?

6x³ / 2x = ?

-2x² / 2x = ?

4x / 2x = ?

Good luck!