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.
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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 = a³In our problem the dunking booth is a cube prism with dimensions: x + 3Side = x +3therefore,V = a³ = ( x +3)³= (x)³ + 3× (x)²× 3 + 3× x × (3)² + (3)³= x³ + 9x² + 27x + 27Regrouping ,= x³+ 27+ 9x² + 27xRewrite 27as 33.x³+ 3³+9x²+ 27xSince 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+ 27xSimplify.(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.(x+3)(x+3)².Therefore, the polynomial is (x+3)(x+3)².Learn more about Polynomial:https://brainly.com/question/11536910#SPJ4