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

Answer 1

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!