Question

the width, w, of a rectangular garden is x - 2. The area of the garden is x^3 - 2x -4. What is an expression for the length of the garden?
a. x^2 - 2x - 2
b. x^2 + 2x - 2
c. x^2 - 2x + 2
d. x^2 + 2x + 2

Answer 1

Have you ever done polynomial division?

Answer 2

no.

Answer 3

You know that the Area (A) of a rectangle is the Length (L) times the Width (W) or \(A=L\times W\)

Answer 4

That means, the Length (L) is equal to the Area (A) divided by Width (W) or \(L = \frac{A}{W}\)

Answer 5

okay.

Answer 6

The problem statement gives you your width and area, can you write out the problem using the equation \(L=\frac{A}{W}\)?

Answer 7

L = x - 2/x^3 -2x -4

Answer 8

Close, you just need to flip the two, you have W/A and you want A/W.

Answer 9

L = x^3 - 2x - 4/ x - 2

Answer 10

Okay, now let's put it in a form we understand.

Answer 11

ok

Answer 12

Now since we have only two items out front, let's look at what it would take to get the first two terms under the division. So how many times does x-2 go into x^3-2x

Answer 13

3

Answer 14

Well, 3 * x-2 = 3x-6, and you cannot take that away from x^3-2x.

Answer 15

But what if you multiplied it by 'x'?

Answer 16

how do i do that

Answer 17

What do you get if you multiply x * (x-2)?

Answer 18

im not sure how to do that

Answer 19

You would multiply x*x and x*-2 to get you x^2-2x. But you cannot take away x^2 from x^3, so you will need to multiply by x^2 and try again.

Answer 20

What would you multiply your (x-2) by to get an x^3?

Answer 21

Okay, I'll do the first step. You have (x-2) and you are trying to find as close, without going over, as you can get to x^3-2x (because we are just looking at the first two terms.