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Question

The volume of a cube is given by the polynomial p(x)= 27x³+54x²+36x+8 find the possible expression for the side of the cube

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Solution

The volume of a cube is given by p (x) = 27x3 + 54x2 + 36x + 8.

As you know that volume of cube = (side)3

So, p (x) = 27x3 + 54x2 + 36x + 8 can be reduced in the form (side)3.

This can be done as,

27x3 + 54x2 + 36x + 8

= (3x)3 + 54x2 + 36x + 23 [Recall the identity (a + b)3 = a3 + b3 + 3ab(a + b)]

= (3x)3 + 3 × (3x)2 × 2 + 3 × 3x × 22 + 23

= (3x)3 + 3 × 3x × 2 (3x + 2) + 23

= (3x + 2)3

So, p (x) = (3x + 2)3

Thus, the side of the cube is (3x + 2) units.

Cheers!


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