Question

The volume of a cuboid p ( x ) = x cube + 13 x square + 32x + 20; find the possible expressions for dimensions of the cuboid.

Answer 1

Let p(x) = x³ + 13x² + 32x + 20
Put x = (−1) in p(x)
p(−1) = (−1)³ + 13(−1)² + 32(−1) + 20
= (−1) + 13(1) − 32 + 20
= −33 + 33 = 0
Hence (x + 1) is a factor of p(x)
On dividing, p(x) with (x + 1) we get
p(x) = (x + 1)(x² + 12x + 20)
= (x + 1)(x² + 10x + 2x + 20)
= (x + 1)[x(x + 10) + 2(x + 10)]
= (x + 1)(x + 10)(x + 2)
Volume of cuboid = l × b × h = (x + 1)(x + 10)(x + 2)
Hence the dimensions of the cuboid are (x + 1), (x + 10) and (x + 2)