Question

Need help pls will give you a good rating.

Answer 1

Answer:

x+4

.....................

Answer 2

Answer

$\boxed{x + 4}$

Option C is the correct option

Step by step explanation

Let's find the expression which represents the length of the box:

$\mathsf{length \times width \times height \: of \: prism \: = \: volume \: of \: prism}$

$\mathsf{lengh \times \: (x - 1) \times (x + 8) = {x}^{3} + 11 {x}^{2} + 20x - 32}$

$\mathsf{length = \frac{ {x}^{3} + 11 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }$

Write 11x² as a sum

$\mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }$

Write 20x as a sum

$\mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)}}$

Factor out x² from the expression

$\mathsf{ = \frac{ {x}^{2}(x - 1) + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)} }$

Factor out 12 from the expression

$\mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32x - 32 }{(x - 1)(x + 8)} }$

Factor out 32 from the expression

$\mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32(x - 1) }{(x - 1)(x + 8)} }$

Factor out x+1 from the expression

$\mathsf{ = \frac{(x - 1)( {x}^{2} + 12x + 32) }{(x - 1)(x + 8)} }$

Factor out 12x as a sum

$\mathsf{ = \frac{(x - 1)( {x}^{2} + 8x + 4x + 32) }{(x - 1)(x + 8)} }$

Reduce the fraction with x-1

$\mathsf{ = \frac{ {x}^{2} + 8x + 4x + 32 }{(x + 8)} }$

Factor out x from the expression

$\mathsf{ = \frac{x(x + 8) + 4x + 32}{(x + 8)} }$

Factor out 4 from the expression

$\mathsf{ = \frac{x(x + 8) + 4(x + 8)}{x + 8} }$

Factor out x+8 from the expression

$\mathsf{ = \frac{(x + 8)(x + 4)}{x + 8} }$

Reduce the fraction with x+8

$\mathsf{ = x + 4}$

hence, x+4 is the expression that represents the length of a box.

Hope I helped!

Best regards!