Question

The width w of a rectangular swimming pool is x plus 4. The area A of the pool is x cubed minus 13 x plus 12. What is an expression for the length of the pool?

Answer 1

solve using long division

Answer 2

try again

Answer 3

To find the length of the pool, we first need to find an expression for the width in terms of x.

Given that the width w is x + 4, the length L can be expressed as:

L = x + 4

Now, we can use the formula for the area of a rectangle (A = L * w) to find an expression for the length:

A = x^3 - 13x + 12
A = (x + 4)(x - 3)

Since A = L * w, we can set it equal to the given area expression and solve for L:

(x + 4)(x - 3) = x^3 - 13x + 12
x^2 + x - 12 = x^3 - 13x + 12
x^3 - x^2 - 14x + 24 = 0

Now, let's factor the equation by grouping:

x^2(x - 1) - 12(x - 1) = 0
(x^2 - 12)(x - 1) = 0
(x + √12)(x - √12)(x - 1) = 0

Therefore, the length of the pool can be expressed as:

L = x + √12

Answer 4

To find the length of the pool, we first need to find an expression for the width in terms of x.

Given that the width w is x + 4, the length L can be expressed as:

L = x + 4

Now, we can use the formula for the area of a rectangle (A = L * w) to find an expression for the length:

A = x^3 - 13x + 12

Since A = L * w, we can set it equal to the given area expression and solve for L:

L*(x + 4) = x^3 - 13x + 12

Expanding the left side:

Lx + 4L = x^3 - 13x + 12

Substituting L = x + 4:

(x + 4)x + 4(x + 4) = x^3 - 13x + 12

x^2 + 4x + 4(x + 4) = x^3 - 13x + 12
x^2 + 4x + 4x + 16 = x^3 - 13x + 12
x^2 + 8x + 16 = x^3 - 13x + 12

Rearranging terms:

x^3 - x^2 - 21x + 4 = 0

Now, we can use long division to find the quotient, which will give us the length of the pool. The quotient of x^3 - x^2 - 21x + 4 divided by (x + 4) is:

x^2 - 5x + 1

Therefore, the length of the pool can be expressed as:

L = x^2 - 5x + 1

Answer 5

To find the length of the pool, we can use the formula for the area of a rectangle, which is:

A = L * W

Given that the width W of the pool is x + 4, and the area A is x^3 - 13x + 12, we can set up the following equation:

x^3 - 13x + 12 = L * (x + 4)

Expanding the right side of the equation:

x^3 - 13x + 12 = Lx + 4L

Since we know the width W is x + 4, we can express L in terms of x by dividing both sides by x + 4:

(x^3 - 13x + 12)/(x + 4) = L

Now, we will use long division to divide x^3 - 13x + 12 by x + 4 to find the expression for the length L:

x^2 - 4x + 1
_______________
x + 4 | x^3 - 13x + 12
- x^3 + 4x^2
_____________
- 17x + 12
+ 17x + 68
_____________
80

Therefore, the expression for the length of the pool is:

L = x^2 - 4x + 1