Question

The width, w, of a rectangular playground is x +3 . The area of the playground is x^3-7x+6 . What is an expression for the length of the playground? (1 point)

Answer 1

To find the length of the playground, you multiply length(width) = area

To reverse this, you have to divide on each side by the term we know (x + 3)

The answer would be width = (x³ - 7x + 6) / (x + 3)

If you need help solving this, let me know

Answer 2

Answer:

Length is : $x^{2} -3x+2$

Step-by-step explanation:

The width of the rectangular playground is given as = x+3

The area of the playground is given as = $x^{3} -7x+6$

We have to find the length.

The area of the rectangle is given as :

$A= length*width$

So, length can be found as : $length=\frac{area}{width}$

=> $\frac{x^{3}-7x+6 }{x+3}$

Solving this we get,

Factoring $\frac{x^{3}-7x+6 }$ we get (x-1)(x-2)(x+3)

Using the rational root theorem and assuming a0=6 and a(n)=1

Divisors of a0 = 1,2,3,6

Divisor of a(n) = 1

1/1 is the root of equation. So, factoring out x-1 we get

$(x-1)\frac{x^{3}-7x+6 }{x-1}$

$\frac{x^{3}-7x+6 }{x-1}$

$x^{2} +\frac{x^{2}-7x+6 }{x-1}$

$x^{2} +x+\frac{-6x+6}{x-1}$

dividing $\frac{-6x+6}{x-1}$ we get -6

So, result becomes $x^{2} +x-6$

Factoring this we get: $(x-2)(x+3)$

$\frac{(x-1)(x-2)(x+3)}{(x+3)}$

Cancelling x+3

We get the length as = $(x-1)(x-2)$ or $x^{2} -3x+2$