the dunking booth is the shape of a cube represented below x 3. write a polynomial that represents the volume of the dunking booth. write your answer in descending order. please use the palette below to enter your answer.

The dunking booth is the shape of a cube represented below (x+3). Therefore, the polynomial of volume of the dunking booth is

(x +3) (x+3)².

Lets talk about the cube prism

– It has cube faces each two opposite faces are congruent

– It has three dimensions.

– Its volume = a³

In our problem the dunking booth is a cube prism with dimensions: x + 3

Side = x +3

therefore,

V = a³ = ( x +3)³

= (x)³ + 3× (x)²× 3 + 3× x × (3)² + (3)³

= x³ + 9x² + 27x + 27

Regrouping ,

= x³+ 27+ 9x² + 27x

Rewrite 27as 33.

x³+ 3³+9x²+ 27x

Since both terms are perfect cubes, factor using the sum of cubes formula,

a³+b³ = (a + b)(a²- ab+ b²) where a=x and b=3.

(x+3)(x− x⋅3 + 32)+ 9x²+ 27x

Simplify.

(x+3)(x²− 3x + 9)+ 9x²+ 27x

⇒ (x+3)(x²− 3x + 9)+ 9x(x+3)

Now,

x+3 out of (x+3)(x²− 3x + 9)+ 9x(x+3) .

⇒ (x+3)(x²− 3x + 9 + 9x)

Add −3x and 9x.

(x+3) (x²+ 6x+ 9)

Rewrite the polynomial.

(x+3)(x²+ 2⋅x⋅3+ 3²)

Factor using the perfect square trinomial rule a²+2ab+b² = (a + b)² , where a = x and b = 3.

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